{
 "metadata": {
  "name": ""
 },
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 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Introduction"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We want to generate samples of a given density, $f(x)$. In this case, we can assume we already have a reliable way to generate samples from a uniform distribution, $\\mathcal{U}[0,1]$. How do we know a random sample ($v$) comes from the $f(x)$ distribution? One way to think about it is that a histogram of samples must approximate $f(x)$. This means that \n",
      "\n",
      "$$ \\mathbb{P}( v \\in N_{\\Delta}(x) )  = f(x) \\Delta x$$\n",
      "\n",
      "which says that the probability that a sample is in some $\\Delta$ neighborhood of x is approximately $f(x)\\Delta x$. \n",
      "\n",
      "Let's consider how to create these samples for both discrete and continuous random variables."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Inverse CDF Method for Discrete Variables"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Suppose we have a probability mass function,\n",
      "\n",
      "$$ f(x) = \\sum p_i \\delta(x-x_i) $$\n",
      "\n",
      "where $p_i$ is the probability *mass* at the point $x_i$. For example, for a fair six-sided die, we have\n",
      "\n",
      "$$ f(x) = \\frac{1}{6} \\sum_{i=1}^6 \\delta(x-i) $$\n",
      "\n",
      "This generates the corresponding cumulative mass function,\n",
      "\n",
      "$$ F(x) = \\frac{1}{6} \\sum_{i=1}^6 U(x-i) $$\n",
      "\n",
      "where $U$ is the unit-step function. The next block of code develops this using `sympy`."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import sympy as S\n",
      "x=S.symbols('x')\n",
      "F = sum([S.Heaviside(x-i+1) for i in range(1,7)])/6 # offset to satisfy sympy definition\n",
      "S.plot(F,(x,0,6),ylabel='CDF(x)',xlabel='x');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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       "text": [
        "<matplotlib.figure.Figure at 0x6d63bd0>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now, we want a random number generator that outputs an element of $\\left \\{  1,2,3,..,6\\right \\} $ with equal probability. We can generate a uniform random variable and think of it as picking a point on the y-axis of the plot above. Then, all we do is pick the corresponding x-axis value as the output. Let's do this in the next code block"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "invF=S.Piecewise((1,0<x<=1/6),    # if uniform sample between 0 and 1/6, choose die-side labeled 1\n",
      "                 (2,1/6<x<=2/6),\n",
      "                 (3,2/6<x<=3/6),\n",
      "                 (4,3/6<x<=4/6),\n",
      "                 (5,4/6<x<=5/6),\n",
      "                 (6,5/6<x<=1))\n",
      "\n",
      "samples=array([invF.subs(x,i) for i in  rand(500)])\n",
      "hist(samples,bins=[1,2,3,4,5,6,7],normed=1,align='left');\n",
      "axis(ymax=2/6.)\n",
      "title('Estimated PMF of Fair Six-Sided Die');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Iro3TxNfXF+Xl7v8EEhHdrvhlY06S3sdjfn1Jzi85OyA/vxYs8EREbooF3knS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\nEbkpFngiIjfFAk9E5Kb+P7IwkQQVqghUAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x6dc9270>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For comparison, here is the estimated CDF compared with $F$. You can trying using more or fewer samples in `rand()` to see how this changes."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "bar(-.5+arange(1,7),cumsum([mean(samples==i) for i in range(1,7)]),alpha=.3,label='ECDF')   # estimated CDF\n",
      "bar(-.25+arange(1,7),[F.subs(x,i).evalf() for i in range(1,7)],fc='g',alpha=.3,width=.5,label='CDF') # target CDF\n",
      "legend(loc=0)\n",
      "title('Estimated CDF for fair six-sided die',fontsize=18)\n",
      "ylabel('Frequency',fontsize=18)\n",
      "xlabel('Die face index',fontsize=18)\n",
      "axis(ymax=1.1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "(0.0, 7.0, 0.0, 1.1)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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rF2P69Olo2rQpVqxYgYiICFhaWqJDhw6YO3cujh49il9//RUHDhwAYwzNmjVD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\nNKICQQghRCMqEIQQQjT6/xw7o3mEWR6LAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x63e0730>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "By repeating the same argument, we can construct an *unfair* six-sided die as\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "p = array([1,2,9,2,1,1]) # the faces 2,4 and more probable than 1,5,6 and 3 is the most probable\n",
      "p = p/sum(p) # normalize to 1\n",
      "Fu = sum([S.Heaviside(x-i+1)*p[i-1] for i in range(1,7)])\n",
      "S.plot(Fu,(x,0,6),ylabel='CDF(x)',xlabel='x',title='Unfair 6-sided Die');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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rMXDgQGRlZSEgIACjR49GRkYGIiIimp2fmJiIqVOn4oknnmjymOrFQFX1xWD2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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7872f70>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In the next block, we automate computing the inverse."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "cp=cumsum([0]+p.tolist()) # need to find edges on vertical axis, add [0] to get left edge\n",
      "invFu=S.Piecewise(*[(i,j<x<=k) for i,j,k in zip(range(1,7),cp[:-1],cp[1:])])\n",
      "hist([invFu.subs(x,i) for i in  rand(1000)],bins=[1,2,3,4,5,6,7],normed=1,align='left');\n",
      "axis(ymax=1.)\n",
      "title('Estimated PMF of Unfair Six-Sided Die');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x6d714d0>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Inverse CDF Method for Continuous Variables"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The same idea applies to continuous random variables, but now we have to use squeeze the  intervals down to individual points. In the example above, our inverse function was a piecewise function that operated on uniform random samples. In this case, the piecewise function collapses to a continuous inverse function. \n",
      "\n",
      "We want to generate random samples for a CDF $F$ that is invertible. The criterion for generating an appropriate sample is the following,\n",
      "\n",
      "$$ \\mathbb{P}(F(x) < v < F(x+\\Delta x)) =  F(x+\\Delta x) - F(x) = \\int_x^{x+\\Delta x} f(u) du \\approx  f(x) \\Delta x$$\n",
      "\n",
      "which is saying that the probability that the sample $v$ is contained in a $\\Delta x$ interval is approximately equal to the density function, $f(x) \\Delta x$ at that point. The trick is to use a uniform random sample ($u$) and an invertible CDF $F(x)$ to construct these samples.\n",
      "\n",
      "Note that for a uniform random variable $u \\sim \\mathcal{U}[0,1]$, we have,\n",
      "\n",
      "$$ \\mathbb{P}(x < F^{-1}(u) < x+\\Delta x) =\\mathbb{P}(F(x) < u < F(x+\\Delta x)) =  F(x+\\Delta x) - F(x) = \\int_x^{x+\\Delta x} f(p) dp \\approx  f(x) \\Delta x$$\n",
      "\n",
      "This means that $ v=F^{-1}(u) \\sim f $, which is what we were after. Let's try this with the exponential distribution,\n",
      "\n",
      "$$ f_{\\alpha}(x) = \\alpha\\exp(-\\alpha x) $$\n",
      "\n",
      "with the following CDF,\n",
      "\n",
      "$$ F(x) = 1-\\exp(-\\alpha x )$$\n",
      "\n",
      "and corresponding inverse,\n",
      "\n",
      "$$ F^{-1}(u)  = \\frac{1}{\\alpha}\\ln \\frac{1}{(1-u)}$$ "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import scipy.stats\n",
      "\n",
      "alpha = 1.\n",
      "nsamp = 1000\n",
      "\n",
      "u=scipy.stats.uniform(0,1)\n",
      "x=scipy.stats.expon(alpha)\n",
      "\n",
      "Finv=lambda u: 1/alpha*log(1/(1-u))\n",
      "#Finv=lambda u: 1+1/alpha*log(1/(1-u)) # shift over to correct\n",
      "    \n",
      "fig,ax = subplots()\n",
      "\n",
      "xhat = array(map(Finv,u.rvs(nsamp)))\n",
      "# exponential distrib samples by inverse method\n",
      "ax.hist(xhat,normed=1,bins=30,alpha=0.3,label='inverse method') \n",
      "# exponential distrib samples by scipy.stats\n",
      "xrvs = x.rvs(nsamp)\n",
      "xe = linspace(0,xrvs.max(),100)\n",
      "ax.hist(xrvs,bins=30,normed=1,alpha=0.3,label='scipy.stats')\n",
      "# exponential theoretical density function\n",
      "ax.plot(xe,x.pdf(xe),'r-',label='theoretical')\n",
      "ax.set_xticks(range(int(xrvs.max())))\n",
      "ax.axis(ymax=1.05)\n",
      "ax.set_title('Inverse CDF for Exponential Distribution')\n",
      "ax.set_ylabel('pdf(x)',fontsize=18)\n",
      "ax.set_xlabel('x',fontsize=18)\n",
      "ax.legend();"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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+NzMzQ0VFBaqqqiAQCPDmm29i//79GD16NPbv34+IiAgA1Wk6JRIJOnTowB5b\nVVWlkOqzdlpPAFi0aBGWLVuGsLAwWFtbY8aMGRg/fjyys7Nx+fJleHp6snVlMhlGjx7NSbOJiYlC\n2djYGKWlpazO+tpW9zRf+4ZuamqKvLw8AEBubi66dOnC7jM3N4etrS0ePXqEvLw8ODs7K7RT9xo0\nFWoYtIl8VJKREaT+/jA8fx4GN25AqiPDQKHwnfDwcCxcuBAPHz7EH3/8gePHjwOovuEZGxvj3r17\nCvmga1P3puvg4IDvv/8eAJCQkIA33ngDffr0gaurK/r27Yv9+/c3SWN9rpqG2m6sm8fJyQlZWVls\nubS0FAUFBXB2doajoyNycnLYfYQQhfKLQF1JWuL41l0gFdUBpMIrySi1r06SIT4Si4KLV1Fw8SpK\nUpTzyWoTvvqo+aiLatINrVu3Rt++fTFz5kw2aAxU3yBfffVVLFiwAMXFxaiqqkJGRka9Q2F/++03\n9kZpbW0NhmFgYGCAQYMG4e7du9izZw8kEgkkEgmuXLmC1NRUtW3Vdv/UF9wNCwurt22uaU7l5xg1\nahR27NiBmzdvorKyEl9++SW6d+8OV1dXhIWFISUlBUeOHIFUKkVMTAweP37cYNtcoIZBS1RJJGyM\nQVJegXKX6mGqRreTIS0uhbS4FLJKsS4lUvQYcyMDiGxNtPYyN2r6UNC6T811y2+++SbOnj3LBp3l\nrFu3DmKxGL1794aXlxciIyPZG6Gq8fvXrl3D4MGD2RFAy5cvh7u7OywsLLB//34cOHAAHTt2RIcO\nHbBkyRJIagaLNKRZ1bnkZUtLy3rbnjBhAlJSUuDp6YlJkyY1eL7+/fvj008/xeTJk+Hn54f79+9j\n06ZNAAA7Ozv8/PPPWLx4Mby9vZGRkYFevXqpbbMx0NSeWuLZ5ZvwGBYKgUSM1C17Icx/Cq/Z0ZDY\n2CJ9/S8AAGMne1j7t9etUEqLh6b2pDQETe3JI5iq6uAzERhA4tgGMnNzGBYWQJj/VMfKKBQKRT16\nYxiSH5fU+7qXX9aseuKvXQEjT85jYAAIBKjwqvaXmtxT78vUJnz1UfNRF9VEeZnRG8NQVC6r96XN\ndWNUUuOhIwIBUOMvrPBuBwAwuZvWvFooFAqlEeiNYeAbvTp2BgCQWuu1lMsNg456DHwdB89HXVQT\n5WWGGgYtwchq5jAI/jUMFW1rXEnpd4EqmgOaQqHwE2oYtERC0lUAij0GWSsbSFrbw6C8HEYamojS\nGPjqo+a+Fbn9AAAgAElEQVSjLqqJ8jJDDYO2qFn1kdRZ+reirW7dSRQKhdIQ1DBoid6+ftVv6hiG\ncu9qd5KpDgLQfPVR81EX1UR5mdGpYYiNjYWvry98fHywYsUKpf1Pnz7FkCFD0KVLF3Tq1Am//PJL\n84tsKjVDVZV6DDoOQFMofMfd3V1hfSBK86OzRfRkMhlmzpyJv/76Cy4uLujRowfCw8MVVk9cu3Yt\nunbtiq+++gpPnz5F+/btMWHCBAiF/F/7L/7GdbijZrhqLSo824IwAhhnZYKplYyjOYiLi+PlUycf\ndbV0TeJnxZAWFWtNi9DKEkatLLXSdnMZhRUrViAjIwMbNmzgVD8uLg7vvvsubt68qWVlukdnd9jE\nxER4e3tDJBIBAMaMGYNDhw4pGIY2bdqw65wXFRXBzs6uRRgFAP+OOqrTYyAmpqh0c4NJ1n0YpaUA\nPfx1II6i70iLilFyJ11r7Vv4emnNMFB0j85cSTk5OXBzc2PLrq6uSkvGTp8+Hbdu3YKzszMCAgKw\nevXq5pbZZPq0q14DiRgoGzJ5ANr4TnKzauLbE7AcPuqimjTH6tWr0alTJ3h4eCAwMBDnzp1DVVUV\nVq1ahVdeeQUeHh4YMGAAHj58CKB6cTj5CqQzZszAnDlzMGrUKHh4eGD48OF48OABAODjjz/GwoUL\nFc41btw4rF+/vsHznzx5Et999x0OHjwId3d39O/fHwCwfft29O7dGx4eHujWrRt+/fVXANXLXb/1\n1lvIzc2Fu7s7PDw8kJeXh8uXL2PAgAHw8PCAr68vFixYoM1L2Wzo7PGby7rky5YtQ5cuXXDmzBnc\nu3cPYWFhSEpKgqWl8pPKqv9+BEfn6qQd5pZW8GrvB//u1SsNXv8nHiZCBv4jBgH4d9if/I+mjXJF\n8i1EACAGAiQmV2dj6ulXPentlJk5bAF0v50MSTPpoWX9LT9//py3i+jJ01uePHkSjo6OePDgAaRS\nKX788UccOHAAe/bsQdu2bXHr1i2YmpqqbGP//v3YvXs3unXrhkWLFuGdd97Bn3/+ibFjx2LixIlY\nvHgxGIZBfn4+zp07hzVr1jR4fpFIhNmzZyMzM1PBkDg4OGDXrl3w8PDAhQsX8NZbb6Fr167w9/fH\n3r17ERUVpeBKmjhxIqKjoxEREYGysjIkJzfvwx5X5L+RuLg4Nm2ou7s7wsLCVNbX2eqq8fHxWLRo\nEWJjYwEAX331FQQCAebOncvWGTZsGD777DP07dsXADBw4ECsWLEC3bt3V2jr5MmTENu1rfd8ZkYC\n+Ldpvq7vySVf4c3vvkaFyAv3l3+vsM/4fgZEc2dB4uyCkps3mk0TH/3mAD91tSRNqlbOLMt6qHVX\nkpm7c4P10tPTMXToUPz000/o06cPDA0NAQCBgYH44osvMGTIEKVj7OzscPnyZYhEIsyYMQNisRgb\nN24EUP3kLhKJkJSUBGdnZ/Tu3RtfffUVQkJCsHHjRpw8eRK7du1q8PwAtxjDxIkTERQUhKioKJUx\nhtdeew39+vXDtGnTYGdn1/CF0xEtZnXV7t27Iy0tDZmZmRCLxdi9ezfCw8MV6vj6+uKvv/4CAOTl\n5SElJQVeXl66kNt41IxKAoBKV3dUGZvA8GEOmJoUfhSKPuLl5YVly5ZhxYoVaN++PaZNm4ZHjx4h\nJyeHjS/WB8MwCukrzc3NYWNjg9zcXADA6NGjsXfvXgDA3r17ldJzqjq//FhV/PXXXxg0aBDatm0L\nT09PnDhxAoWFhWrrr1mzBnfv3kWvXr0QGhrKZpxr6ejMMAiFQqxduxaDBw+Gn58fRo8ejQ4dOiAm\nJgYxMTEAgE8//RT//PMPAgICEBoaipUrV8LW1lZXkhtFHy/v6jcqDAMMDFDuUx2DECYkNJsmvj0B\ny+GjLqpJc4waNQp//vknkpKSwDAMvvjiC7i4uCAjo+EMhnXTVZaUlKCwsBBONelxIyIi8Oeff+Lm\nzZtITU3FsGHDOJ1fFZWVlZg8eTLee+89pKamIiMjA2FhYWw2NVXuby8vL2zcuBFpaWl4//33MWXK\nFJSXl3O6LnxGp0N8hg4diqFDhypsi4qKYt+3bt0av//+e3PL0gyyf3MxqKLc1w/mN5MgTEiApE5P\niULRF+7evYuHDx8iMDAQxsbGMDExASEEEydOxLJly9C+fXt4enoiOTkZzs7OsLGxUWrjxIkTSEhI\nYIeu9+jRg+1FuLi4oGvXroiOjkZ4eDiMjY05nR8AHB0dcfbsWRBCwDAMxGIxxGIx7OzsIBAI8Ndf\nf+H06dPw86uerGpvb4/CwkIUFRXBysoKALBnzx4MGDAArVu3hpWVFRiGUZuTuiXRQsZ+tjwupt7B\nKKh2JQFAebvqYbnCxMRm08RHvznAT10tXZPQyhIWvtpzuwqtuMXrxGIxlixZgtTUVAiFQgQGBuK7\n776Dvb09KisrMWrUKBQUFKBdu3bYsmULAOU0mm+++SZWrlyJS5cuISAggPUoyBkzZgyio6OxfPly\nAMCqVasQHx+PPXv2qD0/AIwYMYINfotEIpw6dQrLly/H22+/jcrKSgwZMkThwbVdu3YYNWoUunXr\nhqqqKly4cAGnTp3CwoULUV5eDjc3N2zatEnJOLVEqGHQEkzNWkkqXUkAyn3agQgEMEhKAsrKADOz\nZlRH0XeMWmlvAlpj8PPzw4kTJ1Tu+/DDD/Hhhx8qbX/6VDHDoZ2dHb799lu153Bzc4OLiws7SGXO\nnDmczm9jY4M///xTYdvUqVMxdepUtedas2aNwqgnrpPjWhotv8/DU/p4iACo7zEQUzOIvbzBSKUQ\nXr3aLJr49gQsh4+6qCZ+0NCgSYlEgg0bNmDSpEnNpOjlgBoGLcGwMQb1l7iyc/W8BmF8fLNoolBa\nGgzDqJ3zJB+l+PjxY7z77rvNrEy/oYZBS1y4d7f6jZoeAwBUdqpeDqO5RibxdT1/PuqimvjB2rVr\nMX/+fJX72rdvj+zsbBw9ehQWFhbNrEy/oYZBW7D5GNSHcSo6BwAADC5dYutTKBSKrqGGQUv0da1e\nB4oYqL/EMgdHVLm4QPD8OQQpKVrXxFcfNR91tSRNOlq8gNKCaOxvhBoGLcFIa3I+1+NKAgBpYCAA\nGmegNB1jY2Pk5+dTA0FRghCC/Pz8Rg+hpcNVtcT5zAy8DvUT3ORIAwNhdOAAhAkJEEdGalUTH8fm\nA/zU1ZI02dnZoaSkBI8ePQLAbYFKTfH8+XNYW1s32/m4wEdNukD+oGBlZdXoGAw1DFqCIfXPY5DD\n9hiacWkMiv5hYWGhkwDsvXv34Ovr2+znrQ8+amppUFeSlujbpnrKvrp5DHJkfn4gFhYwuH8fTM0T\nn7bg2xOwHD7qopq4QTXpJ9QwaAmmntVVFRAKIe3Zs/rthQvalkWhUCgNQg2DljifXZO3toEYAwBI\nap5wDLU8Tp2v4+D5qItq4gbVpJ9Qw6AtuPYYAEhrDIOQ/qApFAoPoIZBS/RzcARQ/zwGObKAgOo4\nw717YGry3moDvvpe+aiLauIG1aSfUMOgLWp6DKhn5jOLoSGkvarzUxueP69FURQKhdIw1DBoifMP\nq7NONTSPQY6kXz8AgPDvv7Wmia++Vz7qopq4QTXpJ9QwaAt2rSRul5jGGSgUCl+ghkFL9LOzq37D\nIfgMALLOnUEsLWGQmQnmwQOtaOKr75WPuqgmblBN+gk1DNqigZzPSgiFkPTpA0D7w1YpFAqlPqhh\n0BJxeXkAACLkaBgASOVxBi0ZBr76Xvmoi2riBtWkn9C1krRFVc2opAZ6DOJnxZAWFQMAJG3bwQyA\nwZmzKMv6d9iq0Iof+XspFMrLATUMWiK4lQ2Ahie4SYuKUXInvbpADGFnbg7hwxxU/H0RUvvquRAW\nvl4aMQx89b3yURfVxA2qST+hriQtweZj4BpjqKlb1qETAMDs1g0tqKJQKJSGeakMQ3GlFLnFlQ2+\niiulL3yuv/OfAuC2JEZtyjpVp/s0v3HthTXUha++Vz7qopq4QTXpJy+VK6lULENmQUWD9US2JrA0\nfrFLwzRyHoOcUv8uAACz69eq50IIXirbTaFQeAC962iJfpY1MQEuS2LUQtLGBRJ7BwiLi2CccU+j\nmvjqe+WjLqqJG1STfkINg5bgnI9B6UAGpZ2rew3m1zXvTqJQKJSGoIZBS5wrLAAAkCa4gkoDugEA\nzK9f0agmvvpe+aiLauIG1aSfNNqRXlhYiMePH4NhGNjb28PGxkYbulo8jIxbzmdVlHXyB2EEME29\nA0FZmYaVUSgUSv00+Dgrk8lw4MABjB07Fs7OzrCzs0OHDh3g6+sLOzs7uLi4YNy4cTh48CCqagKu\nFCDYzAxAE1xJAKrMLVDh0w6MTAbTZM0NW+Wr75WPuqgmblBN+onaHoNUKsX69euxfPlyPHr0CObm\n5ujevTuGDRsGOzs7EEJQUFCAu3fv4vDhw9i1axfatGmD+fPnIzo6GgZNuCHqE02OMdRQ6t8Vpql3\nYH79KsowVpPSKBQKpV7UGoaOHTviwYMHGDNmDCZOnIh+/fqpvdnLZDKcPXsWW7duxdy5c7F27Vrc\nuXNHa6JbAueKizAIaNwEt1qUBnRD6307YZ50FZpyJsXFxfHyaYqPuqgmblBN+olaV9KwYcOQnp6O\n//3vfwgJCam3B2BgYIABAwZg8+bNuHfvHoYMGaIVsS0JeYyhqT2GCi9vyMzNYZT3CAbZ2ZqURqFQ\nKPWi1jB89913cHR0bHSDTk5O+P777znVjY2Nha+vL3x8fLBixQqVdc6cOYOuXbuiU6dOCAkJabQe\nXRFsbFT9pqkuNQMDlHWqHrZqcvGCRjTx9SmKj7qoJm5QTfqJRoerSiQSznVlMhlmzpyJ2NhYJCcn\nY+fOnbh9+7ZCnWfPnmHGjBn4/fffcfPmTezbt0+TcrUK09h8DCooDegKADC+QIffUSiU5oOzYZgy\nZQrK6hk6effuXfTt25fziRMTE+Ht7Q2RSARDQ0OMGTMGhw4dUqizY8cOjBo1Cq6urgCA1q1bc25f\n15wtKwXQuHwMdZHPZzCOjwcqGl7KoyH4Or6bj7qoJm5QTfoJ53kMW7ZsQXx8PHbt2oUuXboo7Zs5\ncyYYhuF84pycHLi5ubFlV1dXJCQkKNRJS0uDRCLBq6++iuLiYsyaNQsTJ05U2d6q/34ER+dqA2Ju\naQWv9n7w794LAHD9n3iYCBkMGtCfLQNQ2F+7nHjxAmzNDNkuqfyH1phyakUlwgBAYIDEmiGnPf06\nV7dfU+7nNEChXHd/T7/OqBB5IT4zHWUxMeg9a1aT9dSmqcdrq3zjxg1e6YmLi8ONGzd4pac2fNHD\n1zIff098KcfFxWHnzp0AAHd3d4SFhUEVDCGEqNxTh2PHjmHSpEkoKirC8uXLMWvWLJSUlCA6Ohrb\nt29Hjx49sHPnTnh5eXFpDvv370dsbCw2btwIANi2bRsSEhLwww8/sHVmzpyJK1eu4OTJkygrK0Pv\n3r3xxx9/wMfHR6GtkydPQmzXtt7zmRkJ4GBhxHkRPSdLY06fQx2Wvh0gfJyHe2v/B2lre5V1jJ3s\nYdjK8t98DCqw27sDrffvQmVkJMq+/faFNFEoFEptrly5goEDBypt5+xKGjx4MJKSkhAUFITZs2dj\n6NCh6NKlC3bs2IGPPvoI58+f52wUAMDFxQXZtUbbZGdnsy4jOW5ubhg0aBBMTU1hZ2eH4OBgJCUl\ncT6HTqnJx9CUJTFqU9KtBwDA8NgxgJsNp1AolBeiUXctJycnHD9+HH369MGxY8eQnp6ONWvWYOXK\nlRAKG7e6Rvfu3ZGWlobMzEyIxWLs3r0b4eHhCnVGjBiBuLg4yGQylJWVISEhAX5+fo06j644J66s\nfvOCE/0qPdtCZm8PwcOHMLjxYrOg+ep75aMuqokbVJN+0ijDkJ+fjxEjRuDChQsICgqClZUV5s+f\njy1btjT6xEKhEGvXrsXgwYPh5+eH0aNHo0OHDoiJiUFMTAwAwNfXF0OGDIG/vz8CAwMxffr0FmMY\nwM58fsGUFwIBKvpVx0YMY2NfVBWFQqE0COcYw9mzZzFhwgQ8fvwYX375JT7++GNkZGRg7NixSExM\nxPjx47FhwwaYm5trW7MSfIwxWLu6QlBWhtTNu0BMzVTW4RJjAIDWj7Nh9/4MSLt2RfHJky+ki0Kh\nUOS8cIxh4MCBMDIywt9//42PP/4YAODp6Ym4uDh88skn2L59O7p27ao5xS2dmh7Di7qSAKCiZyCI\nqSmEV6+CefTohdujUCiU+uBsGEaNGoWrV6+iZ8+eCtuFQiGWL1+OY8eOoaSkROMCWypnayb7vcgE\nNxYTE0j617iTTpxocjN89b3yURfVxA2qST/hbBh2794NKysrtfvDwsJw7RrNOAYAIITN+aypnM2S\nmvWnaJyBQqFoG40uieHg4KDJ5louVVUIAUAYgeYMw6BBAADDs2eB0tImtcHXNWT4qItq4gbVpJ+o\nvWv973//a1LiHalUik2bNr2QqBaPfA7DCyyHURfi5ARp9+5gysth+NdfGmuXQqFQ6qLWMMyZMwe+\nvr744Ycf8PTp0wYbys3NxapVq9C+fXt89NFHGhXZ4pBKcQZoci4GdYhHjAAAGB0+3KTj+ep75aMu\nqokbVJN+onaQfVpaGhYsWIA5c+bgww8/RI8ePdCzZ0+0bdsWtra2bAa3tLQ0XLx4EdeuXQPDMJg6\ndSoWL17cnJ+BdzDyHoOGstjJyitQlvUQla/0hBkAYWwsylLTARMThXpCK0sYtbLUyDkpFMrLS4Pz\nGB48eICYmBjs3bsXqampKut07NgRERERmD59Otq0aaMVofWh6XkMTpaGMDFs+KZubmQAS2Nl28rk\n56OVjw+klpa4t3G72uO5zmMQ2lpDWvAcAOD+2YcwvZeGnDnzUdKzt0I9C18vmLk7N6ibQqFQAPXz\nGBqcluvq6oolS5ZgyZIlyMvLQ3JyMp48eQKGYWBvb4+OHTvC3l71InEtlTJJFXKLG84tIbI1UWkY\n5DEGTbuSAKA4sA9M76XBMuGCkmGgUCgUTaA2xvDFF1/g5s2bbDkrKwuWlpZ49dVX8dZbbyEiIgIh\nISF6ZxQ0Qk2MgTRy/SgulAT2AQCYX0kEIxY36li++l75qItq4gbVpJ/UaxiuX7/OlkUiEX777bdm\nEdXS+Td7m0ZHAwMAJI5tUCHygkF5OcyuX9V4+xQKhaL2ztWqVSs8e/asObXoD1IpQgCNLIehiuJe\n1ZnyLBMalwuar+O7+aiLauIG1aSfqPV1dO3aFStXroRYLIaNjQ0A4O+//4ZU7j9Xw6RJkzSrsCWi\nyeUwVFAc2Af2u7bC4nIiGIkExNBQK+ehUCgvJ2oNw7fffotRo0Zhzpw57LbaS2KrgmEYahgAQCbD\nGQC9tdRjkLRxQYW7CCZZmTC7cQ2lNcl8GiIuLo6XT1N81EU1cYNq0k/UGoYuXbogJSUF6enpyM3N\nRUhICD799FOEhoY2p74WiabnMaiiuE8/mGRlwiruDGfDQKFQKFyod9iMUChEu3bt0K5dOwQHByMk\nJAQhISHNJK0FUxNjKNeiYSjq27/anXQpAYKyMlSZqc75UBu+PkXxURfVxA2qST/hPGzmzJkztLfA\nFQ3mYlCH1N4BZR06QiARw+LSRa2dh0KhvHyo7TGcO3euSQ0GBwc3WYy+wEgkOAOgp5aCz3KKgkJg\ndvsWrP4+g6L+yrMX68JX3ysfdVFN3KCa9BO1hkGdy4hhGNRdRUO+jWEYyORPyy8zbIxB8/MYalPc\nqy8cNsfA7NZ1CAvyAXhp9XwUCuXlQK1h+PnnnxXKhBD88MMPSEtLw/jx49GhQwcAQHJyMnbs2IF2\n7drhvffe067alkJNjKHUQPMzn2tTZW6B0ld6wjLhAizPn4OkT/1BaL4+RfFRF9XEDapJP1F755oy\nZYpCefXq1Xjy5Anu3LkDFxcXhX0LFy5E7969UVRUpBWRLQ75zGctxhjkFAWFwDLhAqziziD/4w+1\nfj4KhaL/cPZ1rF27FlFRUUpGAaheaC8qKgpr167VqLiWCiNfK0kLS2LUpbTLK5CZW8DkfgaEaapX\nv5XD1zVk+KiLauIG1aSfcL5zZWdnw9zcXO1+MzMzZGVlaURUi6dm5rM2RyXJIYaGKO5d3XU2O/K7\n1s9HoVD0H86GQSQSYevWraioUM5nUF5ejq1bt0IkEmlSW8tFJqvO+dwMhgEAngcPAACYHTn8r1FS\nAV99r3zURTVxg2rSTzgbhg8//BDXrl1D9+7dsX79epw+fRqnT5/GunXr0L17dyQlJSksn/Ey0xwz\nn2tT4dMela5uMMjPh+GxY81yTgqFor9wNgzTp0/HqlWrkJGRgRkzZmDgwIEYOHAgZs6ciczMTHzz\nzTd45513tKmVd1RIZMgtrlR6PS+pwBkAYsKgXNIMw3cZBs9fHQQAMN6yRW01vvpe+aiLauIG1aSf\nNGo85QcffIApU6bg+PHjSE+vTkfZtm1bhIaGsiuwvkyoy/Tm+ry8en8VgwppFUw5pAl9UYr6vQr7\nXVsgPHkSTE4OiIpBAhQKhcKFRg+bMTU1hZWVFaysrGBtbQ0rKyuYmppqQ1uLRVAzj6E5RiXJkVlZ\noXxgKBhCYLxtm8o6fPW98lEX1cQNqkk/aVSP4ddff8WcOXNQWFiosN3GxgbffPMNIiMjNSqupcLI\namIMWl4Soy5lb4yCWexRGG3fjoqPPmqWUVEUCkX/4PxIu3v3bkRGRsLS0hLLli3DwYMHcfDgQSxd\nuhQWFhaYNm0adu3apU2tLQamJh9DVTMbhsoePSETiWDw4AGEZ84o7eer75WPuqgmblBN+glnw7Bs\n2TK0b98e169fx7x58zBixAiMGDEC8+fPx/Xr1+Hj44OvvvpKm1pbDGyPobmf2AUCiCdMAAAYb93a\nvOemUCh6A2fDkJKSgsjISFhZWSnts7a2RmRkJFJSUjQqrqXCSOXzGJovxiCnctw4EKEQhn/8ASYn\nR2EfX32vfNRFNXGDatJPON+5HB0dwTCM2v0Mw8DR0VEjolo6gpp5DM3tSpKVV6BUXFUdhJbJIFj9\nA8qyHiq9xM+Km1UXhUJpWXA2DJGRkdi8eTOKi5VvKkVFRdi8eXOjg8+xsbHw9fWFj48PVqxYobbe\npUuXIBQKceDAgUa1rysYmXytpOY1DJLiUpTcSceTPq8CAMx270Lp9TsouZOOkjvpOHXgEErupENa\nxC/DwEefMNXEDapJP+E8Kqlfv344cuQI/P39ER0drbDs9vr162Fvb4/g4GClBD/qEvfIZDLMnDkT\nf/31F1xcXNCjRw+Eh4ez7dauN3fuXAwZMkQpDwRfYeSrqzbjcNXaVLTzRYVnW5hk3IPlxb85JfGh\nUCgUOZwNQ1hYGPt+3rx5SvuzsrKUUn/Wl7gnMTER3t7e7PpKY8aMwaFDh5QMww8//IA333wTly5d\n4ipV5zCy6nkMt7Scj0G9AAaFQ15Dm/WrYXP0dxQFDwAYBj39OutGTwPw0SdMNXGDatJPON+56ibu\neVFycnLg5ubGll1dXZGQkKBU59ChQzh16hQuXbpUb4yDTzBS3fYYAKC4dz/Yb/8FJpnpME25jXJf\nP51poVAoLQvOhqFu4p4XhctN/oMPPsDy5cvZ1KH1uZJW/fcjODq7AgDMLa3g1d4P/t17AQCu/xMP\nEyGDQQP6s2UACvtrl68mXkSpuErtfnk5KKivyv0JDx/gEICBNcNVE5NvAAD7xC4v93MaUO9+eTkh\n6SpkxaVq98vLfWqelORl29DBaH1gD27s2YaCN8eyx1z85xKMs+zYJyu5T1ZX5fXr16Nz58680RMX\nF4cbN24gOjqaN3rkBAUF8UZPbS180QPw8/fEl3JcXBx27twJAHB3d1fwBNWGITpy3MfHx2PRokWI\njY0FAHz11VcQCASYO3cuW8fLy4s1Bk+fPoWZmRk2btyI8PBwhbZOnjwJsV3bes9nZiSAg4URMguU\nlw2vi5WJAYoqGl78Tl29jssWIn3vNthGRKJs2GuwMTVUebyxkz0MW1mi5E56vecR2lpDWvC8QT11\n6wkL8uH13jSAEKSv2YgLj3PR068zLHy9YObu3GB7zQUfk7dTTdygmlo2V65cwcCByjFInfk6unfv\njrS0NGRmZkIsFmP37t1KN/z09HRkZGQgIyMDb775JtavX69Uh4/IYwzNPSqpLlJbOxT3CgJTVQWb\nP36jMYZGQDVxg2rST3RmGIRCIdauXYvBgwfDz88Po0ePRocOHRATE4OYmBhdydII8lFJVTxYq6gg\nfBQAoNWp4zCgObkpFAoHdBcdBTB06FCkpKTg7t27mD9/PgAgKioKUVFRSnU3b96MkSNHNrfEJqGr\neQyqqPQQoaTLKxBUVuLWds0OINAUfBx3TjVxg2rST3RqGPQVdlSSDpbEUEXBiOpeg2XiRTAV5TpW\nQ6FQ+A4/7lx6hjwfQ3MviaGOct+OKG/niwHl5Wh16oSu5SjBR58w1cQNqkk/oYZBC+gqH4NaGAb5\nNbEGmz9+AyTKWecoFApFDjUMWkCej6HZl92uh9JuPXDC3h6G+U9hduR3XctRgI8+YaqJG1STfkIN\ngxaQ9xj44koCAAgEeB4UAgCw3LgBEIt1q4dCofAWahi0gC7zMdRH54hxqHRxg/DhQxht365rOSx8\n9AlTTdygmvQTft259ASBtNqHz5sYgxyBAfJrlsYw/fZboKLhWeAUCuXlgxoGLcDGGHS4iJ4qEpNv\noDiwDyTt2kHw8CGMf/1V15IA8NMnTDVxg2rST/h159ITdJbzmQsCAYqiZwAATL77Digr07EgCoXC\nN6hh0AKMTMareQxy5GslVYQMgLRLFwgeP4axhpdTbwp89AlTTdygmvQTahi0ACPlcY8BABgG5Z9+\nCgAwWbUKTGGhjgVRKBQ+QQ2DFmCkUt7GGORIBw6EpF8/CJ49g8k33+hQFT99wlQTN6gm/YRfdy49\nQRENbcEAABtcSURBVMDHeQx1YRiUL1kCwjAw3rQJgvT6c0JQKJSXB2oYtIA8xsA3V1LdfAwyf3+I\nx4wBI5HAdPFiHanip0+YauIG1aSfUMOgBeT5GHg3j0EF5Z99BmJqCqPDh2EQH69rORQKhQdQw6AF\n5DEGPiTqqU3tGIMc4uyMivfeAwCYLVgAVFU1tyxe+oSpJm5QTfoJNQxa4N8eQ8u4vBUzZ6LKyQnC\nK1d4tVQGhULRDS3jztXCYKQSXuR8rovanM8WFihbuhQAYLpoEZj8/GZUxU+fMNXEDapJP6GGQQsI\nZPzK4MYFyeuvQxISAkFhIUy/+ELXcigUig5pOXeuFoQ853OVQAixtAqF5RKVr+cVEhSUVb8vl8i0\nrktVjOFf0QzKVq4EMTKC8bZtIH+dRlnWwwZf4mfFL6yLjz5hqokbVJN+ItS1AH2kds7nShnBs3LV\nuQ9MLSVgBGKUFYvhYGkEU0Pdup6qvL1RMWsWTL/+GpafzceTz5cDwvp/Iha+XjBqZdlMCikUSnNA\newxagJFV53wmDL8ur9oYQy0qPvgAMpEIhmmpsD1ysBlU8dMnTDVxg2rST/h159IHZDIwhFQbhRYy\nKkkBU1OUrVoFALDbtxNG2fd1LIhCoTQ3LfDOxW/kS26fFjA6VqKMPMYgK6+oN25Q5NUOxSNGQiCV\nwmn9akCm3fgHH33CVBM3qCb9hMYYNIygBcx6lhSXovz+w3rrVE6ZBpPzf8M0/S5sDx9AwRsRzaSO\nQqHoGtpj0DDyJbeDDQ11rEQZLjEGOcTcHLlR1TOiW2vZpcRHnzDVxA2qST+hhkHDtKR1khqirHMX\nPAsdAkYmRZsfvgEjVj26ikKh6BfUMGgYeY/hLGncmkP1zXcoqZSx719kvkO98xjU8HhCJMROzjDJ\nug/7bZubfO764KNPmGriBtWkn1DDoGHYfM+N7DFUyggeF4tVvgrLpez7CmnzLnJHTEzx8P2PQAyE\nsDn+Byz+SWjW81MolOaHGgYNIw8+B5mY6FiJMo2JMdSm0ssbT8ZNBgA4bVgDYf5TTcripU+YauIG\n1aSfUMOgYdh8z3oQY6hN4dDhKOnyCgxKitHmh2+Ams9JoVD0D2oYNIw8+HxOKtGxEmWaEmNgEQiQ\nGz0LEhtbmN1JhsO2nzWmi48+YaqJG1STfkINg4ZhagyCvvUYAEBm3QoPZ8+rjjfEHoHVuVO6lkSh\nULQANQwaRt5jCDIz17ESZZoaY6hNRTtf5L0dBQBw3LgOhreTX7hNPvqEqSZuUE36ic4NQ2xsLHx9\nfeHj44MVK1Yo7d++fTsCAgLg7++Pvn374vr16zpQyR2BfFQSz9J6apLnAwfj2YBBEEjEsJ0zC8zj\nx7qWRKFQNIhODYNMJsPMmTMRGxuL5ORk7Ny5E7dv31ao4+XlhXPnzuH69etYuHAh3nnnHR2p5YZ8\nye2/Kyt0rESZF4ox1OFxZBTKfdpD+OgRLMaNA0pLm9wWH33CVBM3qCb9RKeGITExEd7e3hCJRDA0\nNMSYMWNw6NAhhTq9e/eGtbU1ACAwMBAPHjzQhVTOMC9BjwEAiKEhcj78DFJnFwivXIHJxEkoy8jW\nWjIfCoXSfOh0Eb2cnBy4ubmxZVdXVyQkqJ9A9b///Q/Dhg1TuW/Vfz+Co7MrAMDc0gpe7f3g370X\nAOD6P/EwETIYNKA/WwagsL92+WriRZSKq9Tul5eDgvoq7WdkMpyBYi6GG2nVfvjOPn4K5Z7ODmzZ\n2FCAdiJflfWv3UpCaUEROvv4QSytwsmrVwEA3Xw7AQCu3LkJAOgb1A/l5RJcuXMTRgYC9PMPAPBv\nT0EeY0hIugpZcSlbrrs/MfkGDCzN8Yqbl9r98vLDxV/h7swoCM6cRsBnC/B4ynSl+jdK8mHsYMf6\nfuVPdLV9wXFxcWr366pcWxsf9PCxHBQUxCs9cvj4e+JDOS4uDjt37gQAuLu7IywsDKpgCCFE5Z5m\nYP/+/YiNjcXGjRsBANu2bUNCQgJ++OEHpbqnT5/GjBkzcP78edjY2CjsO3nyJMR2bes9l5mRAA4W\nRsgsaNjFY2VigKKKhpeeUFXP7uLf6PmfSXjauRsuTP8YpkYGKBerbsvU2QGMlQXK7qTXW8/KyQ5F\nufnVx3Cs52BpBBtT1Qv5CW2tIS14Xu9n41JHXs/w/Hm4Lv0vBFIpnoydjIIRoxTqWPh6wczducG2\nKBRK83LlyhUMHDhQabtOXUkuLi7Izs5my9nZ2XB1dVWqd/36dUyfPh2HDx9WMgp8Qx58jitrus9d\nW2gyxlCb8g6dkBv9AQjDwH7nr2h1/M9GHc9HnzDVxA2qST/RqWHo3r070tLSkJmZCbFYjN27dyM8\nPFyhTlZWFkaOHIlt27bB29tbR0q582++Z/2OMdS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       "text": [
        "<matplotlib.figure.Figure at 0x8dc1d30>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The reason the histogram is shifted over is because we lose knowledge of a constant shift in $v$ because $1-v$ is also uniformly distributed between $\\mathcal{U}[0,1]$. This means we have to change the inverse function to the following:\n",
      "\n",
      "$$ F^{-1}(u)  = 1+\\frac{1}{\\alpha}\\ln \\frac{1}{(1-u)}$$ "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Rejection Method"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In some cases, you may not be able to invert for the CDF. The `rejection` method can handle this situation. The idea is to pick a uniform ($\\mathcal{U}[a,b]$) random variable $u_1$ and $u_2$ so that\n",
      "\n",
      "$$ \\mathbb{P}\\left( u_1 \\in N_{\\Delta}(x) \\bigwedge u_2 < \\frac{f(u_1)}{M} \\right) \\hspace{0.5em} \\approx \\frac{\\Delta x}{b-a} \\frac{f(u_1)}{M} $$\n",
      "\n",
      "where we take $u_1=x$ and $f(x) < M $. The only job of the $M$ variable is to scale down the $f(x)$ so that the $u_2$ variable can span the range.  The *efficiency* of this method is the probability of not rejecting $u_1$ which comes from integrating out the above approximation.\n",
      "\n",
      "$$ \\int dx \\frac{f(x)}{M} \\hspace{0.5em} = \\frac{1}{M(b-a)}$$\n",
      "\n",
      "This means that we don't want an unecessarily large $M$ because that makes it more likely that samples will be discarded. Let's use a density that does not have a continuous inverse. \n",
      "\n",
      "$$ f(x) = \\exp\\left(-\\frac{(x-1)^2}{2x} \\right) \\hspace{1em}  (x+1)/12 $$ \n",
      "\n",
      "where $x>0$. Note that this does not *exactly* integrate out to one like a good probability density function should, but I probably need to think of a better function because the normalization constant for this is pretty convoluted.\n",
      "\n",
      "Nevertheless, here it is with its corresponding CDF."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = linspace(0.001,15,100)\n",
      "fig,ax=subplots()\n",
      "f= lambda x: exp(-(x-1)**2/2./x)*(x+1)/12.\n",
      "fx = f(x)\n",
      "ax.plot(x,fx,label='$f(x)$')\n",
      "ax.plot(x,cumsum(fx)*diff(x)[0],'g',label='$F(x)$')\n",
      "ax.legend(loc=0,fontsize=16);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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nZ7tUHrUvu+r2TEtLY8WKFQBERUUxduxY7NHqPPWVK1eSmprK0qVLAVi+fDnp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\n5FNrshLmZ+D+5AiSo/xsH+q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5e1bkuR63IWVDs9vqjtSRdSSrTc/TEaZNm0ZWluvkORfJ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\nSUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x6dd35d0>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "And, following our rejection plan, the following are the simulated random samples of $f$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "M=.3 # scale factor\n",
      "u1 = rand(10000)*15 # uniform random samples scaled out\n",
      "u2 = rand(10000)    # uniform random samples\n",
      "idx=where(u2<=f(u1)/M)[0] # rejection criterion\n",
      "v = u1[idx]\n",
      "\n",
      "fig,ax=subplots()\n",
      "ax.hist(v,normed=1,bins=40,alpha=.3)\n",
      "ax.plot(x,fx,'r',lw=3.,label='$f(x)$')\n",
      "ax.set_title('Estimated Efficency=%3.1f%%'%(100*len(v)/len(u1)))\n",
      "ax.legend(fontsize=18)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "<matplotlib.legend.Legend at 0x9015690>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Zvx8lOxv7W2+R88orFe6/adMmQ8xGpU7f4WuNfn5+1fIUrRGuJRhHZ2WpFTaO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\n3aCVXrhv0UqnMzSMbe8vJf3vY9Rjlv3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ZNmwYbrebsWPHEhMTw4IFCwAYP348w4cPZ82a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\ngg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x8e34210>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The plot above shows a pretty good match between our target density function, $f$, and our histogram of the samples we just generated using the rejection method.\n",
      "\n",
      "Conceptually, there's nothing wrong with this result. The problem is the efficiency is low -- we are throwing away too many samples, as shown in the figure below. We need to somehow do better."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig,ax=subplots()\n",
      "ax.plot(u1,u2,'.',label='rejected',alpha=.3)\n",
      "ax.plot(u1[idx],u2[idx],'g.',label='accepted',alpha=.3)\n",
      "ax.legend(fontsize=16)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "<matplotlib.legend.Legend at 0x7f357d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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AYM9wmqQiMpTWmGvYZFWZIIorJ/N6sGHQ/xPjjbj319SotxyfiulRsdxeMkru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M2Q152p17eLY7949gaxjj4qhs21Nc8y6boQDUp0xhSurVaJKl7z/N+VApzOeW6Zqm6RisjM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\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SHaSzWo67T2I2iBxzG7mnYx8mvXZVL1HI6cOXWoSC3+cVIhfiKRKSTFDM4I2nSGdzVEzr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\n5jdVSuPDDz+ssgwuNe677z6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       "text": [
        "<matplotlib.figure.Figure at 0x7872ff0>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The above shows the samples that were accepted and rejected by this method. The fact that we threw out so many is very inefficient, and we want to do better."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The above argument uses $u_1$ to select along the domain of $f(x)$ and the other $u_2$ uniform random variable  decides whether to accept or not. One idea would be to choose $u_1$ so that $x$ values are coincidentally those that are near the peak of $f(x)$, instead of uniformly anywhere in the domain, especially near the tails, which are low probability anyway. Now, the trick is to find a new density function $g(x)$ to sample from that has a similiar concentration of probability density. One way it to familiarize oneself with the popular density functions that have adjustable parameters and fast random sample generators already. There are lots of places to look and, chances are, there is likely already such a generator for your problem. Otherwise, the [family of $\\beta$ densities](http://en.wikipedia.org/wiki/Beta_distribution) is a good place to start looking. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "To be explicit, what we want is $u_1 \\sim g(x) $ so that, returning to our earlier argument,\n",
      "\n",
      "$$ \\mathbb{P}\\left( u_1 \\in N_{\\Delta}(x) \\bigwedge u_2 < \\frac{f(u_1)}{M} \\right) \\approx g(x) \\Delta x \\frac{f(u_1)}{M} $$\n",
      "\n",
      "but this is *not* what we need here. The problem is with the second part of the $\\bigwedge$ clause. We need to put something there that will give us something proportional to $f(x)$. Define the following:\n",
      "\n",
      "$$ h(x) = \\frac{f(x)}{g(x)}$$ \n",
      "\n",
      "with corresponding maximum on the domain as $h_{\\max}$ and then go back and construct the second part of the clause as\n",
      "\n",
      "$$ \\mathbb{P}\\left( u_1 \\in N_{\\Delta}(x) \\bigwedge u_2 < \\frac{h(u_1)}{h_{\\max}} \\right) \\approx g(x) \\Delta x \\frac{h(u_1)}{h_{\\max}} = f(x)/h_{\\max} $$\n",
      "\n",
      "Recall that satisfying this criterion means that $u_1=x$. As before, we can estimate the probability of acceptance of the $u_1$ as $ 1/h_{\\max}$.\n",
      "\n",
      "Now, to construct such a $g(x)$ function. Here,we choose the chi-squared distribution. The following plots the $g(x)$ and $f(x)$ (left plot) and the corresponding $h(x)=f(x)/g(x)$ (right plot). Note that $g(x)$ and $f(x)$ have peaks that almost coincide, which is what we are looking for."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ch=scipy.stats.chi2(4) # chi-squared\n",
      "h = lambda x: f(x)/ch.pdf(x) # h-function\n",
      "\n",
      "fig,axs=subplots(1,2)\n",
      "fig.set_size_inches(12,4)\n",
      "axs[0].plot(x,fx,label='$f(x)$')\n",
      "axs[0].plot(x,ch.pdf(x),label='$g(x)$')\n",
      "axs[0].legend(loc=0,fontsize=18)\n",
      "axs[1].plot(x,h(x))\n",
      "axs[1].set_title('$h(x)=f(x)/g(x)$',fontsize=18)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "<matplotlib.text.Text at 0x8e3ea90>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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pVP5MqZpNcukjufRRNZde7b5QTjrqKGSn9Al32TbD/SzOkS8WJ2dwtrDCZdsWQgghhBBq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\nF8Ij1bsbKamso6D8JMUHyzn69X5O7M2HohKCDh8k5NhhgsrLMDc2nvU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       "text": [
        "<matplotlib.figure.Figure at 0x7f66af0>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now, let's generate  some samples from this $\\chi^2$ distribution with the rejection method."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "hmax=h(x).max()\n",
      "u1 = ch.rvs(5000) # samples from chi-square distribution\n",
      "u2 = rand(5000)   # uniform random samples\n",
      "idx = (u2 <= h(u1)/hmax)  # Rejection criterion\n",
      "\n",
      "v = u1[idx]  # keep these only\n",
      "\n",
      "fig,ax=subplots()\n",
      "ax.hist(v,normed=1,bins=40,alpha=.3)\n",
      "ax.plot(x,fx,'r',lw=3.,label='$f(x)$')\n",
      "ax.set_title('Estimated Efficency=%3.1f%%'%(100*len(v)/len(u1)))\n",
      "ax.legend(fontsize=18)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "<matplotlib.legend.Legend at 0x9344c30>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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gWJiu/Sf7VlLu7II7U6fzbcsvv2y1fRFCSGtruWEsbaSpyb6sQgd1oabe+SUV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\ne0IIMQOU7AkhxAz8P1yKwiUnAEFnAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x774c130>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Using the $\\chi^2$ distribution with the rejection method results in throwing away less than 10% of the generated samples compared with our prior example where we threw out at least 80% of the generated samples. Obviously, this way is much more computationally efficient and this is the kind of thing we are always looking for.\n",
      "\n",
      "For completeness, here is the corresponding plot that shows the samples with the corresponding threshold $h(x)/h_{\\max}$ that was used to select them."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig,ax=subplots()\n",
      "ax.plot(u1,u2,'.',label='rejected',alpha=.3)\n",
      "ax.plot(u1[idx],u2[idx],'g.',label='accepted',alpha=.3)\n",
      "ax.plot(x,h(x)/hmax,'r',lw=3.,label='$h(x)$')\n",
      "ax.legend(fontsize=16) "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "<matplotlib.legend.Legend at 0x938fd30>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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d/UnqipzsHkhxzeQSALqiGUo8MroFaw7E6IpmaCr2HCHOcOxFQMfbR1wWBZqK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IwZM7j77rv5/ve/zz333MNHPvIRfvSjH7Fz506WLFlCcXExo6OjfO5zn+Oxxx7jM5/5DDfeeOOU\nY3V3d1NRUYHju99FkGUA5C99ifW9u/nRzqdpC3URTqcIZWIUOnykNYWoHAHBRFYTaGaWRaWrKHVW\nMJLxAyKiIOK0+lANhQ81XEdKlemKtZNUw+RJhdzUdAO7R3czmDpCMOsnkOnn2bZXyGoC6+qXc2Xt\nXHYN9jGSHkXW0xS5SrCKVrpjB3Ba8nHYXNT7GgnLYZw2NxElgoBIXAmhI3BN9YrcaP/RcC+tI29g\nES3YRQemCS6bE5fVw9aBfQRSqdyk5oHsIPtG2zgUOsSO4TfpivST1DJIgoTHmkdWl5lZMAtDGOu2\np3kruWf+On576GVCmRAxJUF9fg0/3vMMTx96haF4nIXlDSyqaMBmsXAkNEhEjp+1t8vxE52be/ew\nvHoxspo96STn8WlKs4pr2TF4mOm+aaS1yROgx9sG/Gj3r+gRBhlKBtENC4JgoSPSTTATpNJTQ0NB\nHcF0/Ky8ad5JCtG5xtl64VwM3uDnCpeuxTGc84nSG264YYqJ/ec+97lJ2w888AAPPPDAGT3gxIlS\n02rNDdv0J3voiLYjqxlq8qbjtru5t/lufndkPfm2IhAEBhLdZN9Se2hGFsniZnbBAm5uvI67Fqzh\nF3te5Gi4HcFewsqaqyl2+iiQCgmk+8iaMTQyGFmdLf6NfPDJA9w193YWlM+iL97Lqrqr2T20j0g2\nhsdajGR1UOdtICgHSapxwpEwFkHEZXXjsLqY7pnO6wNvUuIqQTd0umNdhOU+NL0cv2DDaXVS7CzF\nxGSBbw6jqWBuUnPn0EHCmTCKoVDtmU5v/CjTffVM89UQSLuoza9lJB0ATCyCSJl7bHiovqCWhJJk\nmq+Wlv5dxLU4siqzxb8Dn/OYc6NHctNUOH1S9uipFCjjPzt+ovNMJzmPX6Qblwl2x/pxS66cm+XE\nhWCPfSxLNfmWqsg0j8k5t/rzqcyryA1knSkuuSNewiWc54nSF4+EMLLZ3PYvDm0CU2QwNcBIagDV\nUCl315DQEpgmHAgewW3LZ830a5ldOJu4EiKlREnpESTRQZW7jtr8aaioPHHgVT42dxULyxZTn99I\nZ6QbWctS663DafEgIOKiBKfFi9deTLmnkr0jh2gdPICJwd6Rg4QzIQYTnchmHAs2HFYXZa4yNEND\n0TPU59fzqQV3cefs20jrmVyoRlesg7SaxG0rRtZTxJQgRc5SLIJIMptk+9BuDoWOUu4uJqurCP0Z\n/MkBME164m2k1QSv9T/Hb9r+i/r8aup8VVhEkbgSx251ctucseGh8WLtTwyS0TL0xXrQDYMFpbNP\nOYE5nAyye+QwL3S+kqM0zmTo5kzpg5P9XXPJTAzTyD1GWpPJ6BkUXcEqWClzVmD0yNzY8CFunzu2\n3nDvwrV8d92XmFFY+77zIx9fLLuES9fineC8Gnr1q06W/fw/GNfUrL9tNUVuH4cCnaS1BOJb3zFV\nnmq2DW1kMDEAQFxOYbHY6E8eRdHTgEmZq55ZRfOYW9KIZo65BoYySf5u2W280r0zZwA1q6QBh8XH\nzIIFNPqaCckR6vLqcVqdmKZJd+woZa4KRNFCkaOQ4cwITouHuBpiWl4DomDBbXNT5anhe9d9meFU\nhEg2zv7AIRaWzcPnzEM3BDqjbXhsPmyiDY+tgJA8Srm7kuVVi4krSXTDYE9gH6FMlLyMxJVzr2b/\n6D7C2WFkIw6AKFgYSYYRsFGbX42m6zx67RdzFsFPHnyJLf1bCaRHWVyxCE03KPeU8dWrPzmp+E28\n7V/ftpVXerZxOHQQjy2PhsLpBNNxDJOTxtTl2dxs8x/kcLCf2+asPG1hPZ72GH/8g6N9kx4jnE4x\nlAywpHIBX17xCURBokTJ58sf/IuTnv/7CX19fexKD7wjW+CLBX19fZcomLfwnnZpjONh8X/+AABD\ngH++wkNMTtEW2YfT6sYqSnxi7u2EMjH8iT5UM0NcCaIYGoquIJgiaT3GvKJrcNhcXFG5hIPBo/TH\nBhlKByhzldIXG+XVvhb2je4jq+n8w/K7sFrseCQ324ZaKXdXEkwHuLH+WsJyHIfNSU+sG1nLkNYy\n6LpORkswt3gxSyoXMJgcJZINs276NSyunMGW/n1oxpjKJibH+coVn6A/FgTTjs9ZgGEK6KZKXAlh\nwcHRSCftkQP4E93UeuqxWqxc03wVbaEeDoX3IBtxdDOLjkyxcxo3Nd7Il1d8gqic4v7ld0zyfP/V\nvueQrHZGM8MMJUf4wPSV/POV95yy6G7q2U2+5KUj0kWBw0d94TQ+0Xwt80qnT+Gfx4tpS9+Yu+Ob\n/t1s7GplNJU8ZYEZ96I/HOyftN/xxX5OSR2GaeXe+evwOpwsKG9g9cLl79vCdTxqa2vfsS3wxYJL\nBf0Y3tMujTfO8OX+r1kteO35HI114LR5SGQjLC2/mkJXPoqhYAoCGBZcog/dUBlKduO0uvnHJQ9R\n4PISkROYmNTkV7Ft4E0+MG0l2wZ3MxDvRdZl4mqYvrjJ1zb9iFnF9RimQVKJk1BjlDsrcTucOKwS\ngUwWf6qdCmcjPfIhND2LxSLRHW3HZXXRG+/GbnGwoes19o62IwCj6UBOVrihs5U9I4fI6jKxbJRg\nZohgtodqTzNJNUZMCRDODmKYBjtGNlLgqGJJ+UJi2Qg20YlgWsbSlawVlDtrcNuc/Mvrj9NYWDMl\nQ3Q8uehkFgAwdeBFstjRzAQ3NV1PmbtokvXAyfjncU5cNVSa30piOt65cXwQqi3YRTATRBStNBXW\nTxp8OZ7jPhec98U2OXk8LuWbvvu42N9D57VTrykswPm97wGg2SXW37wCu+jAZXPR4JvJd9fdT+tQ\nG/mSF90QyZcKqctvIpaNoZkKzUVLWFw1D7fk5NcHn+G1/lc5HDyAKNiIZZNopobXnk8gM4KspTFM\nnUB6lJ3Du6jx1mEYAj67j6WViyhy+Xi+cyP9yS5kLUlGjyHrUVQyWAUJWU/TFdsLpshQupe4EsVj\ny2cwOUhCieGw2Nkz0smuoQOohspoapjhTD+aoaAZKqYBuqnitHpJqhFELLhsPrxSAaOHBxEKJIqd\npQTSw8wpuoKKvGpK3CWUuYtPmvYz7rH+6LV/z5XT5p6ww/1+629oC3fSEelB0wU+PncsdcnnyCOe\nTU7ppk+EWcW1PN/xBhlNpj/upyqvgkJnfo7mGknFCKYjuWSiUTmAbugoms79y+/IHftMEoEm+qmf\nCS7mTralpYV1l131nlLw/Llwtu+Ls8GF9h56T3fqz+8b5K63/m9abXxv7QP88cgbOfOqSR7gFQv4\n/NKP8su9LzKQ7MNutTOcGeb5jk0IgoDX7qUjGkEzVZJqhEh2lHJPLaWOUhxWF167j7gcAUGg1FXJ\n3uH9/Ozmb/DtLf+J3SLx+N4nGUz3oBkKIiKGaeK1VZDREhimgcuaB6KHpBolYwYQNOiNd+Gy5VHg\nLEI1dQ4F2hlO95LRkthEJz57McNqD6JgpchVQV3+dDRdxWF1oOkaxe5SEtkkSSWJhxLW1l3FyqrL\neXN4DwtKZ+OxeYhmY0SzYTRD56AxOUP0dL4t69u2ciBwAFnLUOaqxDSPdcfjgzmnGiOfmAsaSgcw\nBBNREClzFaG9teA53kGOe9HbbQ6uKL6SwfjgJB8beOej6yfqqC72TvaSgufdx8X+HjqvnXogbnLZ\n0z8HIOO081/XLuTjzatYXDmW9jPO/wYyYeaXzGJJ1QzmlNRxKDBIMB0klBkiIkc5Gt5HOBsiqYZQ\nzASyGUfAQr1nJkeih2nwzWBB6TyOhtuxCFayRoYPN93Inzq38ubQNtpCRxhO9pHSouhmliVlHyDf\nXsqaurUU2stxWH1Ue+pRTZW0nsA0TBQzjqLJZJQMYXkEECl1lRLLxlCNLBaLDckigSCypGQFq2tX\n4nXkYxVt/OCG/4lXKkbRNQwg5c6yoGwBVd5S7py3BsO0cs/8dSwsb2AkFaPUVUZSSZ21znxTz27C\ncoK+eCeCIDKrcBZz31pwHE/n6Y71nzTCbmIu6GhmFBOTfMnHl6+4awoHP86Xf37J7SSymSn8P5xZ\nItCpurETdVTvNS36ucQlHvkY3s1rcaG9h97TC6XtgxlW/vHXAMgeFy98cPmk2599Iz0klCS1vioK\nHHls7tvHkwdfpsX/KkOpLqLqMIohvxV2YSAgYpg6Y6x0HqPyID5HMYH0MHbRyY9v+iZPHvw9td56\nNva9zK6RFuJqCN00yGgJnDYvFsHBzMI53Ny0hrZwJ8sqFvH1lZ9j32gX8WySmBxAN01MNNyWIhQj\ngy6oyLpMNBtFNbJM982mwlVJubuSq2quRDNM/Mlh9gb2Ilkktg7sxy256IkNoJs6JiaGYXD/8jvY\n0Nk6Jb+0LTiAw2qnNz6I2+biYODMMkT3jfRgtzoYSYW4fvo6snp2SjE8VYTd4WB/Lhd0fmkzhmHm\n1DfHK1LGt5026aRKlXf64TnRl8LJFmUv4RLOFBeauuo9XdRHgwpXPjdmVJPyutl52/WTOriJReCn\nu56hPdTFweB+RjN96IaKQgrRFLEKEiIWDAxsggvRtGKKOnbclHpqUA2F6fnTiWSSHIn0YLVYGUr2\nopsaipEmpYaods8ma6QpdpUhYGX7yG68tjz+0Pl7fr7/t/TGe9DRUfQsshHDQMduySOjx7EJDlJa\nAIfVg2nquKxermtYRb6Uh9vu4kvLPs6vDvyepJoglAkwmh5B06E71klEDhM/MsKPPvG/KHR6pnSj\nHeFBAukIXdEBmgqm0Rbq4ECgjS39B/hA3ZLTcuGBVJxGXyNZPTupK59XOp2nD73Chu6XOBg8RFNh\nE8Wugkk8+W1zVjKSinHfktuIn6T7PhucyYfnVNzpib4ULjQ+9Gxw/LU4kzWJixXvJqc+jgvl+r6n\nOfUC27H/ZwWTjlAPP9n1x0l+5Hc0r2J921a2+F9H1pMICDgteUT1Qay4xqIvjAReWylzfAupdlez\nyf8CBVIJMSXIULKHu+d+ArvVzu6Rw8hamoHkEaw4KJDKGMn0UO2ai4ZKVksTSo9gGCblrkraI+3I\nRgpMiCqDWAQrxY46bOI0vFIhJjoiNhQzjSS6CcsDmBgYhsFzRyxUeStZUr4Ap02izF1GSA6gGDJe\nWwHTfLUk1RQOixN7mcbm3n3c0bxqCr/3i70vjKl6vOV0RfuJyNHckNNDrz1Gva+Kw8EeGgtrcNtc\nk1bvx6/fuLmTW3JNGv7ZMdRKIDNIUg3zSq+HW2fcmDNSu2XmFWzobCUqxyfZAf85cSJ++WLnQyfi\nXNjpXuxKj3eCi82ueBzntVNXIjLz/vAUACN5Nh6cGaYvMUyxq4RA6pjHx6ae3bSFO0ircbyOEpZV\nXMlgYgTDVBBFC5gGomCjqXAO/7r2fl7oepO0lkSyuqlyT0M1DVoG3sCf7KfCXcVI2o9NtJDW4tgt\nLuJagGjWj8tagGR1UOwso8Axthg4kuohqg2gkcVAJ6tlWFqxCrfNjVvyUOGppdZbj26IxJRRdBRM\nTCSLi2JnCW7JyUgqRomzkFg2RYW7hh/c8DVSikyFu5w8u4uKmupJAz9ff/17HAoc4jdtL1GXV0tW\nV3BIDr607OM8ffhFBAQSaorGgukYGCdVx4xjvEN+Yv8GDgXbCWdj1OfXsKFnAzFlBEEQcYgeDMHC\n3OJG7p0/5oZ4rrrgs+mAzrYbu9D40LPB8dfidGsSZ3KdL9Q7m/OxvnAmaz7vBZxtp35ebQJmFx77\nECqCiYFOWknSHenPdV3joQuGaVJgL+OWxpv5t+vuZ3nlNVhECdMwsIkurKKNI6F27lz/Za6fdi0m\nJtPzGyhyFRDNRvHavaTVBA6rHRMd1VQRRSuqruC0eLEKDmwWB9V509FMje+uu59abw1OixcR8S16\nR0HEwuHQXmJKjFJXKd9d9wA3N13LXXM+hsOah4gVmzB2Poqusj/QRlxOctucVdw8Yy0//NA/UZVX\nyB3Nqyh05dET9eMS7QB8deNP+OvnvkVfqp2MnqEv3s6v256kPz7Mvc3XUejysATmmKIAACAASURB\nVLb+GnzOMafGzkjv2Di+zUGdr+a03WpGVxjNBJBVmU29bzKnaCFW0YYoWNAFg3A6BDBJB38uXA7P\nNLj5RKHPp8PpQqMvJpzOpuFMrvN7zbnyvYTz6aJ5PnFe6ZcG7zH+RbdaaPTNp9hRyKMTpHDDySBz\nSprIajKFzkK+tPx2NnS2IggmVa5G4mqEWQXz2BvcRlqPUiqW0Z8cYlnFCpp803mucwP9iSNYLRJl\nzlocFjuYIhk9htPiozZ/Jl3RvWjIqFqGfCmf71//TxS6PCi6AoKAiIRKDBtubBYneVI+6+pX89Sh\np1n9yz/isHm5rGw5Lks+kujEKlqZ5q1nJD3I6mmrCMuxXLbnxNvfpJJidkkDe3a00hHp482hN9FM\nHd1QGU33IIoWaj31hDIh/njkDbwON891vERCiZFRZb6z9kts7t3HZy+7JZfQdKo3o6orFDoK0U0d\ni8XKHN8sHBY7PfFe8h356KbOxByUc5XN2RbsYjA5hN3mmCTJPJ4KGE4Gad99IBcUcra3vxfb7fPx\nHuKnkzeeCRV1PvNWzyXOh5/6xSofPa+d+sQoO7vTS5m7lOVViyd1XTuHDpLRsiytXsT/vvbzOUOq\neaWzqfc1cmXVKuaVzcUEJMFJLBvmstLZqLpG68heip2luKR8BESC8iCGCSXOKiTRzazCBdw5+6PY\nrR58UgUpPcTRcFvuzb6sYiH59iJ8tkqKLU1YceKx+mjwNZHRsoTkAWQ9RVjuZ3P/8xS7yvHaSyi0\nl7OgdDaFzrHBoYnuiM+0vchW/y4GEiO0h7rJqDKSTaLaW05ciTCS6sFtKWR24eWsKF8LImOWCMJ4\n0ZKJZkc5ENzFQ5t+SFrN8lLXTqJynCcOvHrKDnVZxULcNjdXVC3h4dX3MaOwlv/3oX/mrjkfxWvz\nsqJ6Sc4sDM6dJ3d9QS15Uh5NBQ2TfN+P7ywli52sprztLvL93oWeSad5yWf9/Yfz2qlPDJ22O1zM\nL53FtsFd7Bk5RHe8G5+jAEPXcSTtPLD8jkm0gCYnWFw1n3ubr+PFrlb+at7fsLHvVVZUXs7TR/6E\nx57HcGKQpoKZeKR8VC1LWkuM2fnqScrc00irKVKqjMdWQEIJ4LT6uLZ+HQ+99hhpJUVCSeGxeigv\nqkI3dSLZEDc0rEPVdcLpKG6rj0jWD4JJhbueq2pWMhgfxGaxsX1oF1ZRYlXN5bnx/eFkEFOAiByh\nN9rPd679It/e+ksa5s/m+Y6NiKYVMLix8SMsrphDXE6yuX8H88tmc9uca3jiwKtk9SymCbKRpDN6\nlKyWZSjpp9JbTWNB/Sk71E8uXIfP6UEUBH5z6BUkyxjtc8+CdXgdnnele/vqxp/Q4t+Cbmg0FEyf\nQqultTSLy+fnfu6y2d/2eVyoXejJcLad6cXaacKljNJ3gvNa1FGOdZURLcMbAzsxBZPm0pnsC+5l\nKNWL0+Kh0FXE79vfYPNAK2klgyTa0Ewtpyy5o3kVf//C91A1mU19m8AAm8WKLujoporH6qHAM23M\nt9vqYdfIG/QnDiFgRe1QWVt3PX/o+m8+0vQxwpkwHZEOhlN9eKQCpuc1kNEzlLhLyOoyO/x7cNtd\n/NvaL1PjKecXh37J3OIFfOfa+9ncuw9Fy7LV30JCiXB9/Ydx2105X5SdQwfRdR1/vAevzcvThzZR\n4y3HMA0cVie6oDOzcDGhTARREJB1Ba/dy18tvJENna2k1DQemxsoJqFGiWWjhOQRZhcuyH1RfHnF\nHZMmQWU9g6qruTi48WnS3SOHJ4VYTywG50ohsb5tKy3+FlRDRTc0hlKjk2m1oib2Bg5R5io6rf/M\nmeBiLmqXcAlvF+e3U59Av+gWEX+yH6fVSUbL4rC4GEl1oVoUAqkA/2f7D0ipYUzTxCLYKHZVkFRS\nuGx2vA43wUwQf6oLCxKykSKaLWBm0Xzmls5ENwyCmQAVnkrqCmrY7N8AAmSNOH3xNhLZCEtKVrB/\nZD9eu5eR9ACKIROTR3EUziXfkU9SSRKVw2iSwsLyebzY1crfLPswlfmluc7wjuZVPN+xCQMAkZ3D\nO3lo5Sf5xd4X+MPRl+iJtxFXAuTbyjkSOcxAsp9ZRbOx9GVwV7q4qfHDufH6B1//EWE5MiaPPPoG\nKTWDYRpcXXsV2wZ2UOaqoid2BKfoYTDpp9HXyHeu/SLffP0XtPhbEBDIlwqJqREKHUVs7t+B960o\nOcliJ5IJIwgiZZ6SKd39O+Gm17dt5eWeN0grGTRDxzQhrSbIlwr4l5Wfye03biy2uHI+t889Rvm0\ntLQQLBYvye64lMs5EZeuxdvH+e3UJ9AvsmhQ4anGJljY2r8NwTQxANVQGEr3M5TsRCOJQgoQiasB\nkmoc1byal3veoC/RR0oNo5HFikRYz/DmUICDwVZE0crtsz6BAITTUaryGumNH8REJ2EMI2eSCBEb\nTquDtJ7BLrowTYPLylbwr2vv54GXv0dGz5BUo6T1BC/3vEyh8yPAsc5yvJjtCezAItjxSD7umnUL\nv9j7Ar8/8hJdsYPIRhy7JY+w0k8+5VTl1bCscj7+cCffXPsXvNjViqJlueOZf6Arug9JdOOWfDx5\nKEGJqxhZz7K4fD6/vOVhvrbpRwiAKFoIZ4JYLFbWt2+hN96LZuqklBhRJcIM32w0Q2N+2bHgjDub\nV7Nz6ABlnpITpgmdaMHtTLv34WSQsBxBVmVCmQDlngrsspOf3/ytScHYE6mS8TuZw8EeLAMpoqU6\nc4qa0Mwz/1K5pL++hEs4Mc5vUZ/QqWdF0A2N9ugBmgpm05fYg0NwoYsajfkzSGTDxBQN1cwgkYdu\namTUODbBSlrJUOAoxmZxgT4WLqGbKoqZIKvEsOPlmSO/Y27RfK6puZxabwW/7xA5EtmJjoJKgoHU\nXsqcTTT5mql0V7G69hgXvrxyIZv7dzC7aAFHI4fIaBmePryerkg/MwrrckqWsByhJq+JgWQ3fzn3\nLrKmyh+OjhX0qDqISyzAKtpozF9MhaeKJRUL8NhclM6uzQ34PL73CfqTnSiGTEZPUOAqx2F1YAI2\n0UaZq4hCl4dH136BB176d8o8JbSHjjKrqIHRVJBAJozPXoAVkcdu+d9s7dmfM0gbL3QbOluZVVxP\nW7CLzy/56JQCeCJu+ky7d8lixzDG7lWuq19Htac0l2I0EROpkvFjDyUHySvLI62m2Rs4xOLK+We8\n4Hn8+Tms0gVf5C91psdw6Vq8ffzZFkqzokkwM0pcGeVgIENcHUESneRZinho9d/yzdcsbB9qwaY5\nSBsxFDOOphcRzES5rHQubw7vYUXFtfQn+glnhtENjbg2jEWw4LTmUWwvZVF5M2E5RqWnlKXlS+mJ\ntZE2ZEQkim0N3DbzTo6GOllXfxX3LFibO7fxhcS4nMSf6kfVsuTbCzkUaGckGUA3dfLt+RiGgWSx\ncvecO7lrwRqeOPAqIXkUQRTxWMai7VbWfJD/9YH72Ny7LzcxOl6MHtr0U4ZS/aSUMFaLE1VTCLx1\nl3LrjHupyi/NURVOm8Sja7/As+1bKXcVEpbHJkEfv+mbPLr1V3zt6k9R6PLQuLB8ynUfTgYxTIMa\nbzkvdrWesACe6eTm8R3ync2rsYkipskJi/mJkDv2uN7eIlHmKjrjvz/R+U28rheDvPESLuHt4rxO\nlFaPjCA9/zwAB6o8vDSvGEVTsIgWRNGG2+ajJr+RrtAw31p9H/54miuqV3IoeAALElZRoi10FAGJ\ncCbM5ZWLsYkOGnwzyGoqhg4Oq5c75/wFyysXkVIzOCQH985fx586tzCUGCClhymVGvn0wk8DJkkt\nQ39siO+3/hcvd+4kkEyyoLyBRRUNzCmpY/dgNx57fu54KS3NSGoQr+TDI7lZVbOcv7rsQznnwvXt\nr1FgLyaYHWZJ6TWYGFix84n5a3Juift37KSspop8ex6ybhDJhqlxN+CxFaOZWRxWN0fDbYTTCX62\n7795rfcgK2suw+tw0lxax5ySOv6j9UlGU6Ns6dvHN1b99SSq43jsG+nhmSPPcTBwiGgmjVW0YWJO\nmjI8fjrxRMlIMNWvfXHlDBaUN7CgvOGMJ/LGp0LvW3Ib2994ky9ddzdLqmac1UTf8ZOlF8p04Klw\nPvxOLhRcuhbH8J6eKJ1Ivzgc+dTlTWdR6XIWlC6jwlWHy5pHX7yD0UyI3xzcxIrqBXRHewEB09DJ\nGmlsgkRGl7GJNtrDXWQ1hW2DWwhlR8noSWyigyIpj7ZQFy93v8re4TYyqkJHuBPVyOK0FjK7aD5F\nTh91vioEEw4G99Mbb2fX6DZ+deipXDiz0ybxveu+xM1Na7hv6Ue5snoJ8WwczTRQTYXKvAraI738\nYu8LPL57AwD3zL2VUDqAYMDB8E66Yx2o5rHnfWfzaso9xXxu0U14JDeSKFHuquWjs2/CaXWi6gqK\nJjOveDFhOUhKS3A4uI9vbH48dwynTcJtc6IaOsPp4Um/OxHubF6NoWuUeSoJyAFe6d08Rd99vIb8\neH3z+BzBwcAhUkoaRVcwzbf3Nhg/dqHLwwemLzyj7vz46dHjz++9MB14sU+4XsKFgfNa1CfSL1dM\nX8zNM9bygxv+Bzc3XcsTH/0eBc4iCh1ldIQP88Shp3mxewtzSpooc9ZS5KqjwtWAU3ITV+JEslHq\nfDUMJHqIyCOMZjqRjRgOi4v1Hc/zct8GMkaGkbeKXqmrDNVQ0HWNw+H9xOUkt8y8AtVQ0UwNw9TR\ndIVSV2VOIQLkTK6eOPAqt81ZRaOvkbr86XRFO3nmyO/YNrSN1/u340+O8NCmn/JSdwsKGVQyxJVh\nEARswjGWy2mTePCesaGqO5tX47a6+FDjdSSzaT426xbypRKWla+kL9HDcLoXTVeozpvG167+1KRr\nKVnspLU0Tptryu+Ox4bOVnRM+uJd2EU7P77xX6YUwNMN8owX/WJHMQklxhVVSyapWN4uzpQ7Pd1I\n/HthyOZM7RFOhks88jFcuhZvH3829Yvd6crxnuP/ziiYxYs9fyCjxSi2V9MX62FafjUNhTNoKmig\nI9KFbmj4E35ubvogJS4fHZ4ajsb2Y5BFxA6mSSgzQkIJEpb91ObN4WtXP8xvDm6iK3KESDbIdN8M\n3hzew2vrtzEiDzOa7sdl8WARrYwkBzkoiIymgoymwuwZOcSckiYO+Pfy5uBu+uN+7BYbaTVGo28O\n/lQ/XZGjOCxOFpbNZjg9iqwmEUwBj62EJt+skxY/p03CYZX4Y8ef0A2Dj8+6lc8s+Ate7tmMVbRS\n6qhBN3X+7S0bg4l89tdXfY5Ht/6KxeVzc4NFJ1sgHE4GWTd9DS/1bOSG+lU5L5qJcNscdMf6WVTa\nfMJzHeew8+1e8h1ePLaT0z3H41woVc5kJP7PrYh5PzlIXsJ7F+c3o7S3F9umTQBoK1agrV49aZ+O\n8CD98WEyWop8RzFX1awkJsd5ePXnicop7ltyGy19+8h3FNAV6SYiJxFF6//P3nsHxnGe576/mdnZ\nvovFoncQIFjBTrGIlEhKFGVLlqscS5Yl51pOHF87bnGKThKfJM5N4tgpTpTjIpf4OIktWy6SJVuN\npAp7FTtIEL0D2+v0uX9AWAIkWCTRIi3j+YuzmP3m22+577zzfM/7vHQmToINAUc5LslLXBvBtBQM\nW6PePw/Lljg+doau9DgFo1s6N9WuI56Pk9ISjOa7UM0sIU8VKS2OQ3LRneqkI9GDhEQ0F8ewDVpL\n5jKcHSVjZqnz1zOaH6HUU0FNoJ5/vu2zdCaGkSUnY5k4c4oX43b4KfWU8M1Dj7K16yDD6QydiSG+\n94sf0SdkmFdaz5PtOzgTP4GISEeih5yhM5qPEJCDmJhU+mo4PHyWWxpXsrPvaMFxL6Xm+fyNH2BX\n//HLuvAdHekmp+dYWD6f/2fp26fvFdp7lLAnREbL8quOPXTEhqa4/51rsuGn3FdKRssW/N/fiFPg\nlXKnV+LOeK0dCd+og+QMj3wOM2txDte1n7owqaLUluUL/v7oyZ8QyQ+S1Icp0kt5sWc7vzPvvVPU\nGW6HkyNDh5EEiXmlcxlMD9MYWMhgtpsyTy0VvkpiowNYNgTl8erNl3v305XqxOfw4RLdyJKLumA5\nO/p20508hcG4ImYoc5awuxqv5CMnZPE4PCS1BEXuBvpS/ewePEBn6gwNwdlIopN7578Pr+wpqDYm\npIGfeP/DPNt5gO3dezkROcZAtp0TUYUX+39FUC7lRmNl4RFdt3T8chGqpWDaBvNKm6kvqmXvwH7C\nrlK6Umfoz/Ty7h9/hruabiNvTKVITkW6GcoM4j7PPGsyrqScfnKWWef0XqAkmfgOvnP4mSm9Ss9X\nnZyvrCn0ndVzrKy6csni+biS6tGrmSm/nqx/psJ1BtcD3txM/exZ5J07AdjfUo1/89uQJamgvHip\nbzsIINgSMa0fjxzipYFtPHlmJzt6T7K+bhl9qQidyR58zgADqQESWpyskcW2LW5tvB3VVDBMyJop\nlpffSJErSN7Mk9KSZLQUeSuNU/TQUtxCdaCSVyKvIAs+DDuPxxFEFmTOJA9gW5A3ctT46xFEAcu2\nyBhpytwVDKZ7yBpZzsa7UAyT3lSk0F1oWVVzocXbz9peoCN5ipQ+jEYKSXCimTmMgIvWigXc17qZ\nWC7L6XgHsuhkVlETfmeAoNvHX9/8MfYPnmYkOwIiKLpCT2oAh+jis6s+UOhIdDY2SFxJ0VzcWOhn\ner6S5VIt52A8gEXyCTrjfXx21QfojA9foCSZGNO2bYrdRQUP9vN7n77Ys4+h9AgnImfY2Xccp+Qk\n7AlxdOwEhmmRVLUpGf1ENnY1utBcTa/1a5H1z2Sm5zCzFudwXbezqzt9Gnn3bgBOLmri/7gjdMSG\n2Na9hyJnkFfGXkGzVJySB7cYIG9mUIwUPjmEic3x0R7qglWE3aWYpkWRu4iBdD8pLUaJq5x4PsbG\n+nV0JfvwyUUEZD8+px8RkfV1N+ISfIzkRsjqSQ6OHGQ0n8Qn+VGNPH5nKXNCixnInQXbJmdGMC2b\nrJ7DIboYSHdT6akmpkap8FaT0lPE1VGORfdzKnKGCl8tjxz+MU+d2ckjh37CSCbHWC5KWkkhCS4U\nU0HCQam7jrCnAs3U+MWZlyn3l6AaJuvqVhNwBYjnEywobeLAUBsV3jI6U7345SCamWdWqImEkmDv\nQBtZTefl3qO8MnyK+qJagm5fIQBfKiBNFzxf6D6MYZl4ZTfRfKbQ1m4iOE64Tfalx+10y31hllU1\nA+cCaU9ikI5kN12Js4zmxwi6QjSHG+hODBBwesnoCovK5pHWMtMGyYk57x04zNbOA4xmM685uF/N\n3pNvBYnkDN4auK4ljZPVLwNqjJHsCBk9T87I8XTX8xQ7yxBsgfsWfphKbx0l7kpEQSaaHyKuRPj8\njR/i3tZNZNQMSyrm05HowLAM3OJ41npLw81k9CwxZRTFyHMidgRNV8dbtokyDsmBV/ZhomHZBlk9\nzXC2D5fkxuvw0Z/pwSX4sBGQBA8eRxCn4GYg08OccCsBV4AN9TejWRr1/jpSamTcekCLs6t/F/F8\njF1DW9kbeYJ/3P+/OBE5it8dYknZKkpddYScVbx77vuYm60ko2ZJqAn29r+CS3JhmAYBl4+/u+UP\niOWT45SGmuSeue9ibnELH1z4O2S1bMG/5XvHHuOl/n0klARjuegVK1mmU2g4JReHh09ydKyNRD4D\njG9eP9NxgK8feIInzmzDsE3iSnxKQxM4RzloloaiK4TdZRQ5Qywqn09/apDm4gb6UsPcWLUcwzYu\nmNOOHTumzFm3dGaXNLxuBcnVwrWQSE6sxWT8tsokp1uLGVwZrplNgCYJdMTPops6KyoX89ipn5DS\n40iizNbObUiShFNws6RsHVkjzY01awt9PXN6jr0Dh1GMPG7RTWO4Fa/s4snOcRWJW/JiYmBZBj2Z\nbgzL4MhoG83hRvrT/eS0DHkjg2DbOEQHY0ovDkmmxjuXsLsMzagBAdbVrWd3/27e0/Qenu16DtM2\nGEj3s7lxIy/37Uax0tiYQJKxXJhh5TQGOWx0LGSG8x0sr/gAJib3LfxdTo6dZlZRFW1SFNNOgw2L\nK+bz4NJ3TGl6McENdyX78Dm9LCqfy7vnruPUWGfBv6XUU0paS49/iYKD7x15ekqV53Q+K7PDdRwd\naaOuqGaKB8y9rZvYO3iY1tAcEmqywKNP3AC6Ep1olopL8vL1Oz4+bZBbVbWUnQP7WVI+n4+8+nlC\nrkChkrXI46dUKr4orz8x57C7qFAtey0VJNcLP/5WawQyg18/3lT6pf7IERyHDwOwc1ENB2rdmJbJ\nkvJW2qLtZIwEmpknq6doLJpD1shQH6hnZeVSAm4/7dEevrz7W+wdeZFIbhRRcGBhsbnhZvrTQ/Sk\nOrFtm7QeJ+AsxunwEPaUkdJTFLmKaArX8zc3/wEnxwbQbZuAK0RaS2LYGg7c+JxBPrzgHtbVr+LP\n1/8eWU1lTvFsftn5HAOZbnRTR7BFulI9DGV7yRlJbDRk/Ji2DraAThoQceBmeflm/u32PyGj6eT0\nHPXFNTyweAs3L17Fj04+Q1KNo1twe9MabphUUXlOaeLDsi2SSopoPsOnVt1NJJfivtbNRLN5hrNj\n3FC1hNFslDOJzilVnhM0xAvdhzk8fJKDI/voTPSwoGw+SSXFn954XyG4ypLEWDZLWstMoRsmKIi0\nnqPCW8nyqiVkVGVafnlheSOW7eD+xVsKla8nRnsLFMYDi7ewrOrCqtMJ7nSCOllQ1viW7UF6OUzH\nI/+20kAznPo5XNecesPhwziOHAHgwLIWhuc0cVPtWnJGnr50PyAScpczL7wQ3TbwOnzcUncj/ZkR\nQq4Az3VvYzTbR85IkDFHwRbRTI0TsVP4HEWMKYPIkguvI4Bi5nEJLkZy/dQHminxhPnc6nsJe/1E\ncnni+TSR3BhzixdgWQJeOchds+/i91e+g57kCHsHTnB4+DS9iX52DT2LZWsYtk5WT+BzBBnL96Db\neQQkRCREW0Ilg5sQzf6V3FT7tkKbvPM38GRJ4juHf0LWzDGcHWBb5yF29h7jsVPbGEmnCjYFUxtH\n1/Pdo0/QFukkks3yOws3Igku7l+8hV+0v0RGy2DaJvPCs1lS2VxY96Mj3Wzt3U5CGcW0baJKgtXV\nyzgTHZjCWU+3yTjxWjSb4nTiFB3xTmYFGulOjvJy79EpvPx0fPbr2bi8mrz4WwFv5UbbM7gyXNeS\nxsn0y8LqBaTrVrNn8DCapfG2xs282L+bDXVrOT52BsFSWV6xkA8uubUgmzMsnVG1C5M8FiYxoxsJ\nF7LuAcvmhor1aKaKiQlA3lCJJ6PjHiuGyv2PP0RX8jQAmpXl3gUfoSfRh1cO0BRqoj5YwR8/928c\nixynNlCHYihElQgOUcKwxrP0DdV30pk6S6W/hXh2CFPUmRtaSX/6LD4rRKm3ko8uuX+KQdhEkdH3\njjzN0x0vonbG6Cw6g98RRnY4UYwsr4y+gmEbKEaes4k+mkI1xNUkXslLU/EsdvQdJGWkUHSFnQP7\nCXn8hUfxVVVLeez045R4SlEMtVBGD+O0xg9P/oSm0AJi+QjV3ips7AJnPTHGdHTDxGtjuTgnosco\nchezd/gVfBEf88uaL0sJXAmFMeObfQ7TrcX1QgO92Zj5f/H6cc0qSlc1tjJ36RYOjx6nNTQHzdap\n8lUhSRKzwvUcGjqCU3Lyg+PbERHJ6wp3NL+dbx/pImtGsdAxyGEhAjItoQVsaliD0yGTyGd4oW8X\nkiCyqGw5zeFGTkXaCbj8ZIwoggC6meN7xx4m4CpnUckKsnqO/zz6Q8aUYRQzy1i+jwpvA+WeCkaz\nA6TMISq8TSwun4/L6aHCV8rO/p2sq11HV7KHnFZO3sxR42/gzpa1F3z057t30xY5ydnEUeSkg0Bp\nBTF1gNXhTYzmRtFtjZQaZSDjRpZkyn1hVFNFFmWCbh+V3gVs6x3fOFxSPn8K3/zhpVt4ZeQks0sa\niCnJC4L1e+e8k50D+9lQtxa/7GfP4CF0SyfsLppyA7gYfLKXCl8VmqmxpHw+Qaf/srz3ta7unMEM\nflvx5tIve/YgtbUB8Msl9bzkt6n0lnJw5DhD2VFEQcTj9BBw+WgqqudEpJ3ne7bTFjmDIDr5sxvv\npz0aoy/VjYCITBARiWrvPG6ZtYkHl93BsqpmOuJD7B04RF7PsqH2RmoCZVT7KulO9dOdPIllGzgE\nF7WB+ciCk6QaJ2fkqPRXczZ+FN3KI4s+7l/wQRZXzEc3RBBclHoqOBlto8gdRDN0/nnLn5DXNT65\n8v0cHD5LibuUk9Fj/MfBR/j24cdQVCdLK1uQJYmv7vs+famz5MwYcshP2F3BivI1LKtYTELNoJka\nhmVQF2ygL9VDV6IXn9NLwBngj1bfy4rqORimwLzwbEq8Ifb0n5iiQx/NZkirmWm514XljRwYPEOx\npwhJkDg4fBjZ4aQ70Y9uCFPomukwr7S+cO3fXfp2llQ2X7Xqzhnu9Bxm1uIcZtbiHK5v+mWKnzqM\nZiNU+8txS25ay+eS01ViuQSfX3MPPzi+nXg+hmGqhD3F5LQsz3Ye4MubP81fbHfSnexmINOLaeu4\nZA8VnmI8svPVxsc7iCojYNt8+9i3qA028527/j98ThcSAgdGdxN0lpLWEjQUtVDiKuGGykXsGz6C\nIEj4pCBNRQsJeYI8sPQ2DNsi36XQn+7Dsk3yep76ktqCGgfAJ/sZUgeJqf3IkpeMEeN7J/+LqmAZ\n97RupNJbQX/mLKXiLCRJ5tH3fZVnzu5nNBshpaYRBQHT1hlM96FbOhkjzebGTZyOdfLQ9odZXb2s\nkPF+/cATFygiLlU16pGdNBXXFmSShmWgmzrYIAgXZtUTipnJWfZkOgku31t0xgdlBjO4NrisTv3p\np59m3rx5tLS08KUvfemi5+3fvx+Hw8FPf/rTiw82KajnMXE73bx/4QZWqIOJmQAAIABJREFU1SzB\nMA2C7nGd9kTJfZm3HFlw0Z44wd7BbTx84Fv80fNf5W83fZx3zrmdoLsYt8ONADgd47YD/ekBTNtE\nMbJE1C4MW6M3eYZ3P/p7bO/Zi9vhpTW8goZAI6XuCjRDZW3Ncj64+Da8Di+rKjdR5CxBt/IktQyf\nfvrfSChpQq4QPocXSRBpj7fRGeuaEqxUQ6E9eQrVzJHWhhGQeM+c9xXOWVe7kgpvA8Wecm6x1hB2\n+7m3dRMxJUXWSBJVhsmbWfoyJ6gNNtBSNI+T0TNolkZLaBYv9e7ls8/867jFry0WdOgCAl8/8AQ/\nOL79sjYAE+9pLp7NWG4Et+zhzpa1F2jXX4vb4MV01Feq877WeuRfhw789Y55NdbiraJrv9b/L36T\ncUn6xTRN7rjjDp599lkeeughPvWpT7FhwwbKysouOO+BBx5g/vz5LF26lAULFlwwVldXF40vvojU\n1QVA/113cNfbPlRoLnH+47wsSWQ1nUPDR8kbWUwMFDNHWk3TGY9SHajg6MgJkmqElvBCsprC/xz/\nFUfGDhFyleCSfGi6BoJN3krjEF0k1ARJNQGCyA01y1FMg/U1q8kZeaL5DEOZKAkljmlbSILE4ZEj\nnIgcAsFFf6afU7F9pLQY2DZzwgsYysT5/tFnOBsb5KmOJ8lpSSzLREBkdmgZX7n1M4Vy/gVljewf\nPM3a6hs4eOYQPxrcyos9R0hraRJKkqFsB5qZRRa9OEQXG+rXs7R8PtX+SnJGnqHsKAvL55BWM5R4\niyjxhrivdTN7Bk5cUfXou+euI5rPcF/rZvpTUXTLpiU8i4SSxbKZIps7FekrHAdkH18/8FhBmbOg\nbKoy5WI0y6VULJPn5c+LNDU2XnDOm4Vfhx3A6x2zt7f3DdMO19rU7GrhaqzFWwVXlX7Zt28fs2fP\npvHVH90999zD448/zvz586ec9+///u/cfffd7N+//9JXm5Spb5i9HOPVAD7dDv/P23bxVPt2LNvC\nJXnI6DF8roqCt7hHdvLjU09QJtRiWiYv9G3D7fAiCBIDmS4eXPQgj595kqg6gkN0E1MGiCoGAbmc\ntTW30hCooswdHq82dboRBYFoboyEFqPKX8WeoW04RBemZTKQ7iWqjCDYIoqdxmsXo5oaT559lrOJ\nU7zY58UpusmaCcAm5K7kxto1PNt5gHtaNxboDcuyyZkqRXMqMCyThJogmotQ5a9mMHuWImc5ggAO\nQabGX84DS28jr2v87xe/jSw6ODB0hBWVi6f0H70UzTG5cGViLjC+8dlS3DjlPZOpm8lUzveOPE1c\nSZI387zct7+gzJmgZl4PzTJ5Xm16kvYDqbeMXe7P23aNG5gZOVZUvjYDs6uh9nir0F4zypfXj0sG\n9YGBAerq6grHtbW17N2794JzHn/8cbZt28b+/fsRBOHiA04K6k91HyZRAnElSVukk7ypoJsGa6qX\ncv+SLTzfvZuuVCc5PUtGS1DjnU3OzPEPt32OsNfPn299hPbEK+iWRk7PYJg6CjkcosTSsnVIkkS5\nrwrJIVPqLuPQyA6S5iBxvZ99Ay8zlh3l1sYN7Orfz8aG9Tzd8TJDuSGSaoKx/DAVvkYG0qfxSsU0\nh1owYyZ5PYNh5Ai7y7Ftm7HcGAJg2xaapVLnm0dKj1Prb6Y/NcTC0ma+fuAJ9g0eZUFZC/WhGmK5\nBBvqVheULLc33UYkH0UWb+HI2EEai1q4uW7tlN6kTaEayj1hjoydpMJbUvBjGc5EEBGpvkiz54v9\nwKfj3yffVCffZJ2SC9M2C9WvbodrCp8/MZYoCFOqWi8VnCfPq1b2vKGKyTeqsrkSB8vXguFMhAUl\nLVO+qzcTV/vzzOA3D5cM6pcM0K/iM5/5DP/wD/+AIAjYto19iR5nH21vZ9ar/z62/UWiY2fYeNOt\nvDJ2mPbD+0EQ2DfnZSRB5ODeXaTVJHaDSJm3hnxHAlXPcv9PP8MHWz/AT5//L/JqHKPRJKclEXtt\nIsYA9a0LWVw2n9OHjlEp+njnms3sHTyG1aOBYSDPKsLC4OyRw4ye6iZemaArdYp8RwqvI0hoTgVu\nPKTPjGEoeebccDMd8bOMtvWg6knCs+u4vXkL/cc7iPR0E5hdgYHGFtazq2cf81oXE5D9vN+3iu17\n95KstGmLn+Togd2sqVnNlz/yZ+zauYsXehVMPU/prCL8Tg96Z5KaeAWNdQ188ob38tUff5dYPsm8\n5UvAFuk8eooS2cX77xwP9rt27kC3DCrmN9AYquHg3n3AuQxnx44dNBguvKU1vGvujVP+7pGd1CYc\nfPXH3yU0pwqn5KIh6cLlcEx5P8C9qzfhEETOHjnBcq2SHo/KaDbCcFsPN8yuwdM6fgP4k2//I7pl\nEC832DdwhJIxmVtmLePWjRunjLd+/Xrubd3El3/4TW6oa2Vb12ECLeWF8SYw+fxLHQ+7Y6imzpNb\nn+TJ53/BOzbfxb2tm6Zdj4njn7ftYtfOHciizF986BPc07rxiq93uWOnz4VhpymJuKgJnbOXvpL3\nHzt2jI9//ONv6Prr16+/qp/nWh1/7WtfY9GiRdfNfN7M4x07dvCDH/wAGFcB3XbbVJHC5SDYl4jC\ne/bs4a/+6q94+umnAfj7v/97RFHkT//0TwvnNDU1FQJ5JBLB6/XyyCOP8M53vnPKWFu3bmXD5z6H\n4+hRAD7wR+vJL1yODRwc3U1U6UXCgV8uYUvjO0lpKQ6N7sM0dTRLQTMVRFHAJfrxOgLE1EE0K41D\ncHNT7Z3YFgxm+/A7i2gKNbGudlkhW/nYk19ia88vSJtDWJgUOxrQLQ0Bm6TVj5MAZe4mnIKbd859\nFyfGTuGRPJyOn0QURQzLwCm5sWwDCYmGoiY8spdELsor0QPMDS1GNXNsatjIybHTbGlaz/1LbuM7\nh5/hP4//AM3IkTeyVHpqqQnWUT7mombRbI6PnSGej5HU0qyrXUPQ7StsLE4oXPK6Qk2gHFmSp2Rf\nk33NP7bsLv72pe/Rnx7AKbn40q1/eMlG1BOYfI3GUM0VZcl5XZs2E5yYz7GxNpZVtmKYxhWNufWF\nFxgr5XVnlq/nuq/nc18pLrY+V4LroeDmeqkvuB7W4nrBoUOHuPXWW6/4/EuqX1auXEl7ezvd3d1o\nmsajjz56QbDu7Oykq6uLrq4u7r77br72ta9dcM4EJrs0ej1hdNtkLD/KopIVOEUfDsHFwpKV/PWG\n3yfgDGCZBoqZJugsQbXTOEUvYJM3kvgcIUJyDS1FK3j49ofwO/0EXcX4nH5WVy0q9BXN6xq6pVPs\nrkTCjYyXrBHHsgyyVgQZLxYmtmDz+D2PkNGyuCU3iqnQEGyiMdBEc2guVd5qKjzVvL35bdzWuJ7W\n0hbcTi9BOURSi1PsKuZk5DQrahbjcowHZcPUceLAgUxKG+Vs8gh7h17iKXM73zn6XY6OvoIFrK5e\nSTyfuKjT4t0LNlzQf/N8dUl/egDFVC9oRH0pNcTl+pJOh4v1Ap2Yz4a61RjmhW6MF8OtGze+od6i\nr+e6r+dzXyneSK/U6yGIvdE+q1cL18Na/KbikvSLw+Hg4Ycf5vbbb8c0TR588EHmz5/PN77xDQA+\n9rGPvaaLaYqG59V/m6KD5RUL6U4OMJgepthVhYSER/bxoxMvMKuojpOBevpS7eT1NPX+VlQjR11g\nDlk9ydratYxmxtjUsIYfndzGksp5uCMu/nrD7/OFl75BTIkzlBngsbbHyZt5ckYap+jDtHVs28bn\nCIJp4xS9eGQ/P33/d6gJhMf5a1+YI8Mn2Vi/Gp/Ly5amlTx5ZjeCQGGT8tNP/xtZNYthqqyf9TaK\n3UEqvCW8f+GGgq1BXldoDs/hZOQYuqljkCJljlLibKIh2EJ/+iwdiTbOxI8Tdlfw7Vee4sGld16w\nWTldgJgIHhOZ1UB2EJfkwuf085c3fYSft+3i+c5dBcuDeaUt3P/zv8QnewrZ/NXkXyesEEZNjb7U\nMF/c+LGrnuVNl0VOrMNEhixweW5/hne+ON4qG62/zbgk/XI1sXXrVtb+7kfw9vcC8OWvf5n73nM/\njxx6kiMjJ0moSWJKhGJ3CT7ZR9AZpDJQxrau7STUKC6HF83UaC1pZVX1corcPlwOJ9965X9QzDwi\nArOL53Bj7Upe7N1DR/Is/enTiEi4RR+CKKEZWYrdVWT0OE7Ri2bmcclePr7oo1iSzalINwkljmqq\nrKxazCdueO+UH/1EoMwZCpqhIUkOGopqOTZ6gk0N6+iI919gb/tA6+18+Im/4ODosxjkEXAhdgsE\nWyop89QgIKKjYpgqli1wQ9VqPJKbpuL6wngdsR6aiuvxO31TAtVE8wpbgJpANSdHT/Hdd36RsNfP\n1w88wcu9++lItoNts6B0MZqZR7dMckaO2aFm/uX2TxXGeb2P3JPfm9VzWLb1mmiN6R6zLzafK6FN\nruScK/m814KGuB4ohzdCH11NXA9rcb3gtdIvb2pFqTiJfvnImi2IshO/00dLeBYno+2IiJiYLCmf\nT6WvjP849E0k0UlKi1DpaCSjR9kz/BJZPU+lv5J5pU0oZp6x3AB5MwWCSEOoDrfkJqXGsGwT1cqQ\nM2P4pFJK3DWoZo575t/P9p4XsQSTrJbhG8e+zdKKVZyIHEE1VXwOLyF36IL5D2cinIq2kdGT5Iws\ni0uXE/YWsalhHTY2Q5lBMnqaxlAdsVyCP157Dx7ZyW2zbuZEdB+aJeOTikHWcDs85PUMaSNB0FmC\ngETQ6SepJjmeOkZcSdGd6uTo6LjhWVxJMb+0uaAQmQjo3aluVDNPT6qHe+e9bwp9Y9om5d5qil0h\nbmlYzXeO/YCMlqI+OIu/vOkjUz7X+QqU6YLa5Nd8spu4khxX9pS0YNhp+lLD1AUr33CWdzEP8SvJ\nIq/knCvxKP9t9TH/bTUQeyvhTfV+mf2TxxCyWQD+eJGT/+raQam7mDJfMbNDDQxnIySUJE2hRvYN\nHSGqRNEslYwRJ61FUa0MmqkwpgwRdpbzQs92EkqEnJnCJxa9GljHuKP5FvYO7UdEwrA0TExsTFQz\nx6LSG1hTs4S0ptKb6kYSJdwOH2fix4kofWS0OHkjx8qqNSSUHGdjg4VCGdOyOTh8CBOTGn8D1f4q\nVEPnue6t7B7YiWKouCUPjUU1PLT+/kKA/Z/jz9GX6kIx0ywr30Bz43yi+SgOh5PbZ92Jqmt8aNEH\nSCg5+tLdRPNDqIaOiUmxp7TgB99QXMd9rZt5qn0vP2t7lp50D17Zy2Cmi9lF8+hJnfNymVdaj24I\nLCxr4U/WfYj9g6eoDtQwkBrkvfPuZCyXnPK5Mlq2UGy0o/foeItBd5C0eq793OTClsMjJwh7QnQl\nexnLx6gP1fDZVR8gms8QdPqmeNNMLkA6v51e86xZF/xfuZiH+JXY0F7JOVfiUX4tfMxnim3OYWYt\nzuE3xvslYqRJqAJ7h1/hztmb+J8TP6MneZakPkpGSyIIAiPZTkwMSlx1mFgoWpq0OV4EdGh0J07R\nQ85MolqZ8eYYuSjlvjp+eOqnlLjK6De68Yh+yj2ziKsD+OUwCS3O3Qs2cGfLWu5//CGWVy2nPXoG\nh+hAS+dQrBQ+uYgDw4f4wk2/W+DHE0qamkA5i8qX0B4/w0Cmh5SepDt5DLcUJKOPEnKtwiW5qPBN\n1ZInlDgOyYVL8nE6foTVFTdT6qliVc0Kwt4i/mbDR/HITnTD5MjYfgJyGASbuUVz0TFZXX0XtZO0\n6MOZCLYw7jejmSo3VGygN9OFZqg82pYmoaanUDWFghg9x9ubb+ODrbde8LlCnnHp4x8/92/ElSQ9\nqS4UI8+q2uWFjHdyFrysvJWEmmRF5eLCXsJEljedNw1MpYtawk0XzYB9spuuZB/LylunvH4lWeSV\nnHM5Tv3nbbvI6rlf297ADGbw68Sb26N0cju7VyXwEzaySTWJYmYwbZ2x/CAJNUaFtwnRlpkbXsD7\n5r4PxUrhFkOYqFR6GsiaCSz08QIgwcQWTM7EDxCUi4ioIzglJwvLVoMNHqGItBahwldJXtd4qfco\ndcE69g7sJqbECDlD2NjMLV6DQ5Cp9dbwiV/9I/sHj5FUswUVyr9u+SweyYtiZBnJ9pKxxojqnaik\n6E2fwsQqWO9OPMKrpoppGThENx6Hj8FTZ7mv9d0sKG3iY8vuKvQCFQUodVdS7a/FFgQQIOgM8gfL\n30XQ7eN7R54ueL/MLm6i0lvJo+/5ZzbUryKpxBAEkWh+jEODx6aoF4YzERaUtSCLcuGGczF1Tc5Q\nyJt5SrxllHhLpyhyJituPrx0C42hGj55w3t5YOltUwLfxdQlEzejyb1Op/P4iCtJFpS2FFrrXW1c\nTqEynIkU2vA923ngouNcbZ+VGb+Tc5hZi9ePa5ap39ayCd3lwi2PN4+QRAcCIj4pTNhdhYhA2FuC\nhQmCQMDlY03lFo7HDhGU60ibaVQzAwg4cGNYKgIgCi5G8kOItkh9sIWYMsqi8CJ2Dm9ncek6jozu\nZ/N/f4iMmUI3stiCiYADWXQSdlWRUmN8YN49HBs7RV7P45HcxPMJ5pU0FFQVpZ5SjkQj6FYW4dXr\nj99YbPpS3fzty99lTkkDB4dOoJgqNjYVvlpUI0/YU0G9EZpS6v985y7iShLTNmkqakYxFdwONwvK\n52KYBs92HiChpKZk1nM89QXO/v4lW/jx6V+Q09NElRE6Uk5aK+ZOybANJc2KmnGLAbh4trqmeikv\n9+1nccV8PnnDey9wbJycdU/IRs/fSLzY2E7JxeziJnoSfXx586cvaT52LRUYV3r931befQbXN95U\nTn3Wf/4nwqtim9n/8g2WVLfwcu9RVFOnzFuOZtjMKV7IzXVrSWpZEkqc2aEWxrIRUmqWM/E2VDOP\nbikEHEVkjRSWrVHrW4BmqfgdJcT1AfJGDlGQkASZ6kAtyyoW058eIa0lGct3IQgSEa0dxU5i2Aq6\nreKVinHJblrC8+mIdzGY6SelJbi5fj1/ftOH2dN/zjgrq+cZTg+O2/QKJWh2HpcQoNRTg0OUGcmO\nkdJy1AZrORtrZ33tGmqCtQSdIbbMWsdntnyoQIv8yfP/xM7B5xjNDxNwFrO5cR2qaaCYGn2pAWoC\nVYRcAV7q3U9XopfaYBW/u/TtU/p9ypKEogkcGztJY1Ezpe5SllbMZ0X1HGB6nnk6w62ft+0ipqRI\nazn+aM0HCbo9PHzgR7zUu4N9Qwc5NNzN5lk3FHqfnm8cNcGXn4r0cfeCmy8I2vNK64nkUnxuzT0F\no7PpuNNr3cLtSq9/tXn3GR75HGbW4hyua05dsKxzB6/+ACayorC3iB/d/RV+cHw7o9kIq6qXUuEr\nIa6kUYc0MnqaoVw7CCaSLZPVU5R56snqaRpDTTSLczg+dhBRl9CtPJZt4tGDeBx+cqZKc2gOg7lB\nHHkPuqkiIGKjYWEj40U3FLAEhjPDlHnKcEouKn2V1PjLeabjQIGTXlm1mL/b9P+y/vvPYegmKhFm\nBZYjAC6HiwpfFaIgElfiyILMu1ruIKEmCbp9hcx6gmvfN3iUrtRpDFMlbyYYSAfIGgqRfIx5JS2c\njJymwlsyTkeUtXBk+GSBPjkf9y/ZwpHR01QGygi4fIWMfLJi5XI4n3a4p3UjOS1PWktjYZJWz3VV\nmi6bvVzm+kzHgSnZ/XS+7XDtFRhXev0ZvfsMrke8qZz6BGxZHu/OwIWVkRPHn7jhvdy/5Db8Th+W\nZTGaG8GyDbBFJMlNSK5gTngBq6puIqUmEGwBQZBw4kW10+hWjqbQHOqCVcTzCVZWL6KpaBYufKhm\nmgb3clyU4KGccncTAU8ZC8OLKHYVE1FGUU2V0/GTbO3exc9OP4dtWwxk+jgb78UjO1lcuhIEAxEn\nvZnjSIjMDc8j5CxC1VWyWpa/2fTxAvc8mZvetXMHqqmT03Nk9QSy5CEgV9JasgQbm5yeY2v3C1i2\nhWKoYIsYpjGFPjkfHtnJV277Q1qK66dc67VUCE7Hha+qWopb8lLla2BZ5aLC69P5pV+uUnM63/bT\nh49fdm4/b9vFJ3/5FT7yxN/yzQNPXjc+4W+kenQ6zPDI5zCzFq8fby6nPgFZvmhxx/lZ0uloJyPZ\nYdJanFrfAoZzZ6n0NPDju/+Dl3uOsr1nDwPZXtrih7AtGwMNFz48jhJ6U50EnAFub1rPd47+kN5U\nO5Io4bL9BDwhymnCJbmpDzaxsf5GfnH2VwxkuvE7S5AFkaAzxIGRneSNNIIgUO6pJ56P8tjJF0mp\nGQRBxMbCgQtbEEgoSbwONyFPiKVViwqdkSaaTrdFOmkqrudMtAu/WsnKqsXE1TgdiWOUuqsQRImk\nmmVl1WLaop3MK20mpiSnqFMuFUCmyzAnZ9SHhk7xq7MvXNQfZrrM88NLt+CVXVOqaS92rUtlrpMV\nOCurxi1pf3B8O6qhXRF3Pdn+N+j2z/DXM5jBRXBNgrrtcPDdV35ETI1gA7Zl8uCKOwp/nxzw+9ND\nJNUIMWUAWXAzu2gp33/PV6gJhLmndSP/vO//MJbvxEDBKxRjoCAiY1kmHsnPVzZ/mi+88HXSWpK0\nPopgSzgkJ5qp4HMEMWyDr77tzwi7/fz0zJPMCbcymO5Hsw3SSpyMHqXUXUtcGyWtJ+lOd7Gj7xAb\nG27kbPLoeEWoPd5yTzM10noan8PLmVgHn1jxXuBchjqYGSKtZVixdu14cdItf4DL4eKnbQpBdzG6\nrRHPj78+QUNNqFMmV5FOrM3paBfDmeFLmnhNDrR/8NTfoZgqMTXOF1/+TqGidALnB+opN96Fl6+q\nvBRtMaHAmUwh3du6Ca/suqxt7/n2v2/V8vWZCspzmFmL149rk6k7nST1JIqlYJkG3z7237zUt68Q\nnCZzs5H8GFk9iWXr6LbAYLabHx57nmJPET55vPmFiYqJRs5OIuNCFGRckofF5Yv4wkvf4KWBbaTV\nKNhgY2JbNt2pI4ScNbSWLeeLL36LVTVLmFU0i9H8KPWhJlaUL+JXXc9hZkxcDi+rw5vozfRS5auh\nI9HBnqGXkZApdpdT7q2iN93BnPACvIIHSRi/qUz0FhUZbz/nkt00hOoJuHx8fs09PNNxgMPDJzBs\nHWybWD6GCHzq6X/irzZ+jM88/SVckpMTI2cKQXtibfYMvMKh0b0EncUUuYr54svfYUPDygsqPif3\nHe3L9E1bUXoxPN+9m5gSx7IsZFG8oE/pa/rKp1HgXE7XPoF7W8ftf89/WpjBDGZwId5U9UvT//2/\nANhFRTx75waiuTEags0Uu8MYtkFcjXN8tIfqQEVBVfC/1j3I94//FM3MI0kisuDkZOw07bFODg4f\nJaaOoNm5V2kQGZ9UimIl8cpFZHQV2xbI6lkyegwbKHXVEjcGkZBRzSxj+WFuadhMTs+hGhqR3BhV\n3kqGs6O4RCf1wVm8d847+Pza+zk1Nkhz8SxOR9twOzxElAEkQaQx1IJqquT0HCO5ETJaGo/sZVHp\nfNJahmL3ePu5T658P9u6D3B4zz62xY9wMtLO3JLZKKZOla8SUQDdMomrcdrG+jEsA83SC+vyttmr\nC4qLoewomqGT1hIIgsjX3v4X7J3U2m6i4nNCnRLJxadUlK6rXwhMrfBsjw3wcu/RQrXn46dfJKNl\nMG2TeeHZLKlsft3f/8UUJTt27CDhsqaoSJ5q3zul6tQjO1lS2cySyuY3pbLzWmHHjh0zqo9XMbMW\n5/Ba1S/XZqPU4eCfNn+atTXr+OadXyDgDNCb6iGaH6U5XIdTlOhK9uEWXITdfn5v0e/jkYvQTZWo\n3sVI7iy96bNE8oOEnBWIiJQ6m/FJpahmFo9QRNBZSlZL8srYbjJaDAkHlZ5mAp5iws56LEwsNNyC\nn2NjJ3E73bSUNFJf1MDOwW0cGNnDYHaIjfVreXDFHYS9fr5y2x8yJ1zPnOJ5RPKDeCQffmcYERuH\n6GAg005Gj1HpryKrZdg3dIit3S8RySfJ6Wqhi1HOzJJQE3Qnujk5dppVNcv4x82fxOPwkTNyeGQv\nf3nTR3BKrinHkysd19YuZ2PDBmRRpjk0m88//6/sGzhK6tVyf1mQ2dm3n5PRdrY0rcQpuRBsuGvu\nHXyw9Zw50OTNy21de6dsZK6qWopP9nFjzcpCJ6aL4XKFOJfaVDx/0/V6sX+dwQx+E3FtMvXSUsRP\nfJK3zV6NR3ayvm4Zv+x4mS1Nmzk2cprH258goaWI5OIYpojT4ULVoSN1FBEXGmnyVhzLAM3W8IhB\nfHIRkuBgdeUmBMHJWL4f0zSwbYu8kcLl8GHbFkXOMA5JJqVGqfA00xBqodpXxUPr7ud0dIDne7Yz\nmDmDZmYxTJMbq29keXULcE7bfVP9cn544pc0huYSdBaR1lLElSgZI05DYB6lnjICrgAnokeI5Yc5\nEWkjkk2yq/8kFd4yhuUEpm1yc906llfO54HFWwrrcHy0hy/f+mnCXv8Fxy90H8awTLyym1JPMZX+\nUlrCc+hO9ZHRMiAISEj86Y330ZuKEFdSNBc3klCy3L3g5mkz5cla64SSpi1yhpia5JMr38/KmjlY\ntoP7X53fpTBZt/6rjj10xIam9X45H/X19Rdo5q+F78oEzvemeTOvPZOZnsPMWpzDa83Ur0lQTxX5\n+fqKmsIPJ+j2cGCgnfZYB32ZHjJagtF8D4PZbhwE+cNV72dH7zEG0gOoVgoLnaBQg0Geal8LNhaK\nmWFBeAXF3jALyxbQkehiWeUqzsQPoZHGsDRq/S00h2azpnoVkXwWj8NHXaCOBWUtnIkO8O656/hZ\n2/MopoJhqZR66llbu5KuxAgPH/gRj53cxnOd+3m2aw8D6T6i+SGq/LWsqlpBf3aQUk8dtmDzyB1f\n4JnO3UTzERQrh2apSKLE4opFlHtDzAnPYl54NuX+YlJqhkdPPMuZ6CCdiWE+s/r9hcIcj+ws3Phg\narB7YPEWllU1c2K0l7PxbkzbZFXVUh5afz/PdBzgxZ595Iwc9cEc0gUZAAAgAElEQVTqwk3j/GIj\nmEqL9CRGiSspmopnkVCyLKtqnvY902Hy3EKuAIZlvu6O9tey+Gi6oqoZzOBa4rouPpqAKnLBxlje\nVBjLj2FYJpZtIgoCYVcNnclOHtr+MJZtU+quI5UZxEsZmp2n2jOXCl81kbyDUu8CRpVhAk4/r4wc\nodRdycGhndhYSHgBqA/OQhBEdNvkXS13FIqbbGxGsxE+9ssvotoqqpknIJdSH6wnq6n88NQTdCfb\nsG2bInc5bsmNJMrYtoooOtg1sA/NUBnTBllVsZ7/Pv4cAgIuyc2c0CJSWpqb69cXioImeoO+0LuX\nBWUtBVVMS3jWBQZYk2Wf00kG723dhCyK2DZTDL+utPnxZMWK3+nDtC1OR9up9IbJ69plg+p0DbAn\nK3emU6r8vG0Xz3fvJqflKR118dcfnmoZcC2Lj66lRcGMh/g5zKzF68e1kTTKMoeHT6JZGn3JEcZy\ncdrj7Wimim6qWJaJTypGFl2E3aWYpsGBkT0M59txCyHcjgBl3npKXGHKfGUUu0McGTuEomdIq3Fk\nwY1iZUEQ8EvlGILK0tJ1LCmfT95SC3LCZzoOsL1nLzkjx4rKxTglF+WeSlQ9T1KNIooOXujdxZnY\nEVQ7g2kayKITl6uctB6nyFVCa+k8OpM9nIodQBJk9gy9QG+6F7/sxysHeVfL7bxn/s0823mgEIxj\n+SRdw3HaoifpSLZT46tHswyOjbURdhfx6PEXL/Aqnwj2Fwv453usGHaaFdWLL8qFT/f+e1s3sW/g\nCK3lc4kpySvyM5mskLmz+dw4//uFb1Ere6b1hhnORIgpcRRdYTgSv658U2aqRGfwm45rI2l0yPSn\neij3VzKcHUKx8pS6yzgVO8bccCu6OV7+X+6rICAHiCtxVCuPS/STs+JIlsydTW8j4PJi2RYHho6R\n1qK4HB6iygC2beGVi5EFJxW+WuaWzGdp2XwyRo7+1CACIp/41T9iWgZD2SEGMp2cjZ3GJ/vJm1nq\nAk20hOaSM/PjDo8OP4IpIAoiH130IEcip3GkZBQ9S29qAM3QkUQXhq0g2hIZI02xu5gbKxfjc3kJ\ne6cWy8xbvoSnO7ZTHaglrkRxiTL9mX5umbVhPJi2P0PIFaIn3UVXsptqfxVhd9GUzPlSJflXEpim\ne79HdrKqZskls+zzkdPyKLoCwEQPLY/spKm4dspm5+T5OSUX1quWEbfcfNs11Z1Pd3O73A3m19UV\naSYzPYeZtXj9uCZBXROhOlhLXInTn+6hiRbcTjdeyU9fqpOYMsT88EocooMvbPg9/u7l7xLOVKCb\nKqWOEOWeGjoT3QiI1IdqMG0TzVBIGv2Y5AjShGhLuGQvNcFaMnoGj8tNqb8Yn9PL7sGD9Cd7iKmj\nZPUkZe5axvJ9RBUBw1aYHZqH7HDjwWZpZSvra1bxi85nuK3xFj668i4e2tpHRk+T01MMZ0cYSPUg\n2gKmZVLsrSSjJTEsA6/DiSgIfP3AE4VqUr/Tx7vnruPg0HHSapoz+eMohkJKjfPU2V8yKzSbYleI\nnJmn1FNGzsizrLJ1SuY8XXXmZFxJYLoYzfBaM9VVVUvZObCfJeXzpzwVXIrGmI4yerMx2X/n/Keh\ny2HGnXEG1zOuSVCPm+PZXYkrzE21azgd66Qn1cOo0osgQEAOM5jtJW/kuPW/7iZnJBBtGZU0Nd65\n9Gc7KPGUIwkS7oyLm2tXc2D4JRR9DJBJ0YtHWkCRsxjNHLf7lQUH97Ru5DNP/ys9iS5iyhAtxUs4\nGdlPQouiWVm8jlIyxhjb+h/DLRThlNwICKypWcGyiiUEXF5+cHw79cFqjkb86IZKd+oMsuDGKXso\nlspwSBKzfLPpSraT07N0Jk9i2CqmadAQXMjmplt4+Cf/yc3LVvLI4e9jWgY5I4NuqbgdXlqKmxlM\nDyNoIosr5hOQ/STU5AXGWZcz+LocLha8Xyuf/eGlWwh5/BeMc6mbw7hd8Hgh07XiTicCc87IcWTs\nJCuqp94cL0dv/Tp49xke+Rxm1uL145oEdY8ngEtyceusG9EtC8u22D+8E8s2MM08aVvgQws/yvae\nbQgCaPa4bzkIjKk9mJbFK5GdLC5dgyw5ODx6gryRQsA17pZIEZqep89opyd9ipUVG3jHnLX8vG0X\nkfz4D7XEXUlWT1PmqSVvZilyljKUbQNsbEyy9iia4WX38Fa6U114ZS9JNUNaTdGd6qDKV09MGaHe\n30RUjVLuqmQw04cLm+HsEM1F8xBFgbyZRrOyCMBorp+ueB/31a3jZ737GVOGSWsRJEFmZeVGFpUv\nJOj2kVS9nI2dYSw3yi2NN1/QgWe66szX/B1chc3ISzlAXm78P9/6CP3pAZJnRliwfOm0FgdXE+cH\n6YnAfH7npgm8UXprBjO4Vrgmksbhukri73onDyzeQld8mF+0P8tguhPL1jHRuanmHTglByPZEUbz\nfRi2ilcqwYETh+DGFixKnLU4JCcg0pFop8bXzGi+BxkPDtGNW/QhSU5UK8NYbpT2aIS2aBf96X5S\nahy37COjJYko/SS1ESRkdEvFRMUgjo2GgYFgiSBI1Pga6E31EHAF8cp+cmaGzQ2bGUgPsa72RiwL\nNtSuZzAzgm5pmLaJW3ITV8YbYJe5G1lWuZp/ue1zLGyZw2OnthFRoti2TZW/ibvnvoOh7BghV4Ct\n3dsp9pYylO3jVOQUTsnN3oFT3NK4ElmSLiv5m6y1/uGJ5/ivo0/xy/bdrK9bdlWD0BuR/31p9zcZ\nzg2R9KRpj41xx+y1V21e0+H8uU7o9h9YvIWVNXMukG1eSis/nRf91cCMNvscZtbiHH4jJI1uj7/Q\nxu2XZ7eT1pOE3dUM5dqYFVzK3NLZDKaGub1pC4+eimJTRbmnhnJPGS8PPYUTDwY6tf46zibP0Jdq\nw+MIMCu4DAmBuBYjq8dQtAx+OUzQWYZhGCiWimrm8Dr93Fx3E4+3/xTD1tHJkrdS+B1hdEPBQAZs\nwEAjS41vFik9iSw5EWwLr8PL8solDKQHqfJXs3twL+9qehttsU5SWhxJdFDmKSGmxFlXtRHJ4cAt\njVes/vz0Tu5t3cSa6qUcGtlLwBmmvqiB98y/mR+d3IZq6pi2QVv0CLZtIQgifekubNvmsZMvcv+S\n8dZxE86Pk+mB6Xjig0MHKfGWXdTE60oxWYbodXiYW9rE0ZE26opqCLp9V0xDTMxxJNePKDhwiA6W\nls57XXN6LTifMrnck8RMNj6D31RcE5uAupKqKQ2UI/lBsnqCsKeBm+o2EXT7WF65gNPRswScRUiC\nREqLsW9kO6WuemSHm7CzlEOje9AMBZcYoMrfSI2vDlFy4JMDLCq5kRJnLdW+JmzL4FT8BIOZAbyO\nIsrcFXQne2ktXQGARwjhFDyodg4REQH3/8/ee8fHcZ/X3t+Z2dm+2ILeQaKwAOwUKVKFoiTSKpZk\ny3Jsq9nJtaPkOrZjK4o/uUlex9fvJ9c3Pde+sR2XN8WJYjuOJTmyRFpd7ARJESRIEL0Du9jed6e9\nf0BYAiQgQhJFUg6O/hAXszszO8A++8x5zu8cJBxY8VFnW0sgM0a5vYJdDTsxm6zcVr+NFl8dbaUr\nSGspXLKLp3p/wZlQJ1k1RZHZzURqkl3Ld6IJBiISSSXFyclOnu97mUf+z+/xwOpb2FyxjdUla1lZ\n3Mze/nbMkoUTk51UOKqxSDbuX/Hgm7bzIhpaQV0C8/ukv9B/gNeHj9Id6eJ44BRWs5Va97I5VgPv\nFDMyxGguysnASd7wn6HOU00kE6XSXlLIT51tETCfdcDMebtNPhJKEI/fyYdX3/SOz2s23sqqYD7/\n97fC5fZKXwyWPMTPY75rcbkzYX9VcdV06jDdPTX7ljMUG6DWVc9ybwOJXJLHNtzDz7sPMhwfxp8a\nJqZOYhLNuMQSAtlB3HIZGT0NQDQ3hUW2cWPNDYzHJ3DITkZTo7jMDlrLNuK1eAlnwvjT4zjNRaia\nQlpNgQCpfBqvpQpVV9ANHa+5Et1QSefjKCjc2/wAR8eP0uBuoDvSzUh8mHua7+DBtdO0xw9O7GEy\nMU5KSZBRUjgtHkyCBUVTeGDFfSSVFIqu0Fa2gvaJk4wlRqh01uCzedjb345TtjOenCjY9Npkc0En\nLokSQ7FB1pVtwTAMNpa3XVJdMhMaXWIrpdjq47EN95BRPsDXXv8Bf3zTb7wr3nq2DLHOU0+Dp7bg\nNvmPJ5+fl3+enb16KtDNijdzW+s81VS5a1jma8JiaIWUpXeLt+LBr3aa0hLePZZUR4vDVQvJgPO3\nuP7kWgKpAAOxIf521xOFBTo1RTUMJ88BBmbsJLUw9c42YvkgWTVNJDtO1ohgVYp58uw/sLnsBjZV\nrEczVDpDJ/FaS1BUlTOhdhyyl0guRKtvLcOJYdJqkqyWxWstRtHypNUU0dwEkijzUNun+K1N97G3\nv51mTx0vDO5DFk1ohkJvZAiYHvQNxYcIZ4OsLl5Dx9QxwpkAKTWEzWTnhL+T7VUb2VG7lXA2xqaK\ntbgtbmqKKnHVOhAQCGaCBHMhbizZXihsMzrxmQHeB1u2zVm4NAOHbGUgNsKGsrbCzy4MjbbJZmyy\n+R1TLrMxW4YoCgKvj7YXjr2QGmTmSwYDErnp4OxadzXhdJRbam+YVvVUTr/mcmi/38vVoJdbmz7f\n/pbUHucx37W42oHk7xdclUFpR10xP2vwsKZsGRsqG+kNT87xHGkra+CHHc/RFepkKjNEmaURDYUK\n63IMCWTRilm0ktHjGLqIRhaL5CKWi2Igo6FTai9nLDFMKDuFRXKQUEI0eVpxykXE8zFUXUMUJFwW\nN4YBZY5KEEw0eVZyXWUb19euoq2sgdWlDewfOY1uGHgsXsYSYzx5+j85EWjHafaSUhMouoosWcjr\nWXJ6GgOQRAsDkWFq3FX0R0d5/PoHuaflRqZScR5qu51DY52MJv1ouoamG3zp+o/PGYLODPAW8mzZ\nN9yBz+YhmU/xXO9Bnj73Kr2RQWxmB09se6jgH/N28FZmVrIkFexvD4yeLhx79tDxwsGtPxFnIjnF\n5qp1LHPXkcyncFjsfHn7Q6yvaOS5vkN4LC7OhcYIZqLvyi8G3lvPmMvtCbPkMfP2cbUDya8W3heG\nXsMrl9O+pr7wx/yvp39JKBMink/w2c0PYJPNdIfG6Qr3Ue1sJqkm2FJ+I26bl+F4Hw656M3kIi9J\nJYBN9OK2lvGhlo+wqbyVKmcFNtnOZDpAua2SUG4Su+Qimg9yXdX1yIKZZD5Jib0Mr8XDN+/6I05O\n9rGufA1NxQ08unZ3oaDJksStDZs5MHKGkfgwZyOHiClhMkqceD6G2+xjWdFyvDYfGSU77TUjyCSV\nOOWOSt4IdKDoKkfHz7G7cSsbKhs5fPAgUYuOSTQzFBtmW9UmeiMTBe/whZQVf/jid/mnjp/zi56D\nlNlLSCsZ+mOjhDMhzkW7Ed/8TxItCxaJ2fu4UA2z2EJzoTJkoXNeXdqAbph4dO1u1lc0zvlAypJE\nX3iC3jfOILjN9EdGsMvWd+XM+F6pUuDyO0fOt78lD/HzmO9avJe/32sZ7ws/9a74EL/o20MwFeXH\nna8SSk8RygZpcNext78dmDaXiuVCDERP4ZLdrCtbzYriZkrsVTS5m8hoCSYyPThMZZgkC62+Virt\nPj7auoNPrt9Ni6+On3z4b6h2VdNYtAq7uYg7l99LMpdAFmVK7WX0xc4xkZrgj1/+O1b5lrPMXTnv\nIM0mm9lRv5mhRBcqaZLaJAoZ7KYi7lp+B+srW2n0LsNt8bKm5DokJFZ5W5FEiUg2RF+0i4nkBL/3\ny2+QUfLsG+4kpaTxJ6fY3XALkiTN6x1+4WBoNDHGUHyIE/6j/KLvl1Q5y2graUYUTeTUDH2xcyiG\nQjSTJKPk+cMXv8snn/oTPvPz/0U4nQRgNDFGVssxmZ7ka6//YM7xFgqOvvA8Fjt0nD1snG/waJYs\nhYzSr93y2NsaZF5pvN1B65Xe3xKWMIOr0qkfbHDwWrObnnA/0WwaXTDQDA39TRri2Z7DTKUjHPMf\nQxRNaLrBmWAXVslGSskwmhwkkg9gFi2YRBmfrYJyZyXD8QleGDhCJJPlgdU3U2S1cWvDZg6OnmVd\neRs+u5svb3+In/e8RkpNkVJSJPIRwtkQ3eF+NpSvZTQRLNjsTsTj9EcneH24g1eHjzKZniCvZlDJ\nUWpuotGzku5oH2WOcoqsDr5682PsGznJLbU3M57yIwgCiq5RZq/EYrKg6iovDRwnICfw2TyMJSZ5\ncehFusI95DSNz133a2/ZOQ/HJjgbfoO8lqHKVc/K4kZMkowsmZEwU+WoY31ZK8f9p3mxv50TUyeQ\nJQuxfLSQnPSLnoNEchESuThbKjdwNjhaoFoWur298DxmLHkvTCh6ux3UypI6DsTP4ba46I9O8sDq\nm6/ZAne5u8T59rfUpZ/H0rU4j/dFp45sIaVEmcqM0j55kHQuRYm1mD+//Qvs6Wvn79r/gZ90PYWu\nKyhqBlkyUemowRDAKTvI6XmKLVVk1RSGAfFckEgmSlZLo+o6z/e9XOiKbbKZv9j1ORK5FBIiT55+\nGbMoM5Xx40/1M57pZiR5CqvsQBDmSvf2jx3lH0/9lNdGj3Bs8iDpXAwDA7tQQl7N0R09xdrSNUQy\nUR7bcA8+u5OtVRtQDZVNFWu5Y9kOPGYPp0OHOT11jKSapKm4nrSS5uSbLpUNnkYEAwTDKNylzODC\nzvl/3/Y57CYXLb42DMNAEKY7vmZvHd+++w+4uX4LqqGi6ApNxfWousJofHCOnPF/3/Y5mjyN3Nt0\n50V3CDPd9J6+9jmd+UId/GITihaSos0Yf81YH1+ulKMl6dsS/ivjqnTqfevbONroxSTZqHTUEldi\nfLjlTiZTEX7WtZeO4GESSgQBCQyBhqIWhpM9mEUbkXwYm2Qjng9jN7vxmEuwSDYmMyNIyBgYiKJE\no6+ePX2HebrrVZ7ufpVELkmx3Usil+Rk4DSaoRPJTKCRQyFLMD3K6akBDo4dZDw5gsdSjNvsYiI9\nTjA9RUqJk9ACiAhoKEiijE1ykFAyfO+Df8yevnZeGTyBYRh4rW5+ff2djCaC/KTrx4iCiKLlyKsq\nK4tXoA0luHnNDYTTMboj3eho3FR3A59ad8eczu3CztkmmxF0J/5UmM1V6/jU+jvn8Nkzz690lHFs\nshOrZEEQZP7uzj+i3OkGzgdvnA2OLsgRL7T6cnYH/1TXAV4aPMRAbJhqV+WcOcSFeCuu/md7foHo\nsVzWlKP36xByiVM/j6VrcR7vixWlm5bdyLpSkUAqgD89jiTJvDi0HwEB1ZhWpWS0KB5rGToa0XwI\ns2gnqcSpdlTz0ujPMEt2FC1DUgpjkeys9G1gTVkrxyZOcH3NdbgsDjwWF4dGj5PRMoQyQXRDZ1P1\nWkrtZSSVBAOiCZNuRUKi3N5CJDcKhohu6PRGO3HKW0E3iOdC5LTU9BhSkMBQsYp2PJZi/uHePy0s\npPrP3r2EMiFUTWUqHaEz2A2CSFZNYZWKePKBb9I+2sV1K6q5bd0tRHNJEkoKVcsTTId44sVvkM5n\n2FK5nk+u3z2vtvqRdbvpjQzTGx7is8/9GddXreeRdbsLRd9qMhPQ8owlR7m1fgcCBq8PdVzkw44h\nUu0q44HVF7skLmb15dsJ4ngrKdqtyzYw5eGyrtxckr4t4b8yrkqnbr7/Pm65/zOomkQyn0OWLAzF\nB+mPdRHM+BERMXQdh9lLOh/HLFkxRKh11SEIAhOpERQtjUYem1SESTCDILKmdDXbqjdyeuoc0XSS\nofgIA/E+bCYbO+puQhDAa3ETSIXwpyewS0WE8+NYRBdpNY5gGGiGis3kxG0pIZCZIG8opNUYVY5G\ngrlBVHJUW9ewrfpmvvfBrxY64H/u2MPRyX2F4j+enkIWZIqtpWRVlf/4te/T5KmgrayB5Q0NAHQG\nhhmOjaOhk1NzJHJJUmqKydQU7RM98+Z8ypJEX2SC3vAgSSXJRHIK3TAVutFXBk/QEehiNDnKQHSQ\nVcUtPDKri35l8AQnJs9wNtRNJJskq+rsG+6Yc5zFSMc6/IMk8knqPNVv2aXDW0vRljc00BseZ/9I\nx2XLBZ19vJk7qMu17wtln+92rjAbS53peSxdi/N4X3Dqot3Onr520moGQZgu4Iqeo8Xbhkv2sKFs\nKzbZjSSIgMBUZoR0LsZEfBxZNFFmbcAk2qhzrGW17zpWlWygxlVHub2YpJJmdUkzU5kAY8lxDF0n\nq+aoc1UQSodpn+yg2l2NWbRQU1RPjWM1AuA0ealxrcZqKsJnqySaC5FRUthNTtaVbCOuhLGLXpxS\nKY3eJm5ddv2cFZpNvlqskh1VV4gqAXJKGtVQSasZHmp9kNcGTl7E7zrNVkbjQwhAWskwkR4DYF3Z\nKmqLKhbkq82SBc3QwIC15avmdKNmyUIkG6XaWU2Ns4bxZGDOEv6Z7T3Rs7T7D/P1Q39JJJOYl1t/\nq855IfXGfHz2pfa3WG5+sZh9vHfL+1/qXC/3uS9hCe8WV8cmwGYrxKBpqkKJrQSfzUd1UQWvDydI\nqxl81nIqnJXUuhrwpydIKylC+UlC/glEUWaldxP/9+4/4UvPfx1/ahIBiOdSmETT9FBPtlKkF+G1\n+lhTtop9I8cwBIhkI8iCzH3Nd/HK8AEyagKL5MRl8XJX0x0UyQ5+fO6nrC7eyECsCwwdi8lKibUc\nm8mJquWwyc5CIZ2hMzr8XdzVeA/P9v2ce5s/xKvDr+AwORER6QyeQ9M1joydxGoyI45k0GttTGXC\nqGhEc1GKraWsda4no2YoMk9/WYSzsQVDJkyCiCBwEX3yibadHJs4TYWrFJfFgWgIc5ZWz2wfSvQj\nICAJMnsHX+K+FXe9LapioWX3i1nKPXs1ZX3Mgtn93tEli6ViFrsE/cL9PXn65ct27kse4uexdC3e\nORZV1J9//nl+93d/F03T+PSnP82Xv/zlOdv/5V/+hT/7sz/DMAxcLhff+ta3WLt27YL7M+x20tnz\nMWjXV6/no607+Mor3yOYnuRM+AgOyYfVZGO5ZzknAvtJqUEkbJTbGrBKNvzpUX77P/8fDAwiWT8O\n2cOB8XbuXL4Dj62aGlc5/3T6x7gFL4OREVRDJZPPUGItZmf9ViK5BG6rm42l12OIoBkaNW8GJ58N\n9VHuLCWaDaGjo+h5Gt3NpNUUsmTm9obtBYfEZD5FZ7CHUCbEqamTrCneQE+oj1pXPbqhMZkeJ5AW\np5Uu7uUE0jnUSByr10MwG8IhO8lrOf5m95f48ZmXODF5hhcG9+G1ebmxZuOcoj1TDGenKF2IGbXP\njMPghSHQM9s/9JNeTKIJq2TjrmU7eXDdbRcd550siV9MEZ1dQEdHIjxxw29e0hHxnZ7TYt0WF1v8\nL9zftezm+F7F7i3h2sYlOXVN07jrrrvYu3cvf/AHf8DnP/95duzYQWlpaeE5qVSK3//93+eLX/wi\n1dXVPP7443z605+es5/ZnHr+kUcY83qZTE1xXeV5FUdfZIKD4wfJaQlUcrjNJbitHibT45gEGzk9\nRUqLklAi5PUMgmBiPNWHJMiIgkSlo5qVJY1Es3H2jR5jU8V6zoS6CGdCOMxORFGixFbCCwMvczJw\nGgkTCSWOKAjIJjNf2PKxgrY9mI4TTMeQRBMGBrfWbSeva6woXs7BsRO4zUUcnejghYG99EbPohoa\nFfZqokqUSC6IphtEciEqHFXEcmHMogUEgaQSY3vrTcTyCdaWrcXQDf7+7q/gszvp8A9yeqoLBIFm\n3zJK7T42VDYC0x/Qn3XtZSQxQTATIpZNYDVZ5lV3zNZAz8dny5LE3Y230BkY5i9u/11uqG99S/VL\nW1nDW1oIzMZi+fgZ5c3ndz34lqto3+qcFoPF6ssXuwT9wv1dTv365eaRL4cKaLG/98uNJU79PC67\n+uXIkSM0NTXR8OZw7+Mf/zhPP/00q1atKjxn27bzAQdbt25ldHT0Lfdp2Gx8ct3Wi2LQzJIFt6WE\nuBKkxFrL7uW78FrcnAudJa0l8VhKMQkmIrkpUmqEcHYcWbQiCiZWF6/jr3c/XvAkH4z10xM5hyAI\nSKKJc+FOiszFbCpfwzH/UdJKnLG0ygr3SkRRpN4zvZrVajIXumFFU+mPdtPkXckzvXsI54JIkzK6\noXLcfwjFUHCZPAComkosH8Nj8eK1eFF1lbyeZTg+QFKN0expxSG7+PZdX+H1oQ5+Z/P97O1vZ03p\ncn585iXMkmVOdunLQ6/SG64lnk3yyLrdBZviSDZCWkmyrnzNom75F6JJfHYnO+o3F479ibad7Olr\nZzIZ5NhE50U+6bMdF02CyKPrd72t483GO+lu32tFy6+ii+PluGZLzojvP1yyqI+NjVFbW1t4XFNT\nw+HDhxd8/ve//33uuuuuebd9CmgAck8+ievoUdasWVP4UH/9X79DIB1mdVkrrb41lIRktqjVbN+6\nnTOhXo4eeg2ftYixkilUPY8+mKfI4sXdXEE8H+T44Vd55Nw4ap2Mw2RnrLMbh1yErdGDqisYQzmW\nlZXRHx2h0l7Jue4A66rXI5Y4mcoEOHzwNa7b/DGG3NNugq8feAEwUKs1bJKV7hMnyGpp7I0+dHTy\nfXHyWpZkfQSn5CXRM4kh5wjX+VnuXkm6L0SDq5K+onEeaLyDQ/tfo7WqmqNjXRw/fISn9j5Flauc\naLnG6tJm+o8eZ/R0D44KO/vGXiTVF0GzJ9F1gyKrk5FTfVgzOqpHod61jOde+hnbq7fChulu6sD+\nfciizB89/FlssrngRz3DS873+MC5A1S3NRLNJvjzf/t7kvk01W2N1HmqOdP+Bp/ecG8hfOPQoVfJ\n6zmWr23ljUAXp79/4m0fb+axTTZTEzVx7PCRws9mtgdLRCaTQUZO9XHrsg3cdsstANTHLIyORPjC\nx3/zbR/v/fL41KlT/PZv//Zl21+9asFeUs19K7bPudZvZ0c8CwoAACAASURBVH9mx/QXw2TXENc1\nVTOD9/p6fOtb32LNmjXX1O/nSj3et28fTz75JDB9x7Jr1/wN1EIQDGN29MLF+OlPf8rzzz/Pd7/7\nXQB++MMfcvjwYb7xjW9c9NyXX36Zz372s+zfvx+v1ztn24svvshtt98OQKy9nf/ITzKZDHI2OEiT\nr5Zne/fitngRBLi7cScui6PAB87w1lOpKTqChyi31+E0exlJdOOSvSSVCDbJhUW2Es9FkUSJeDYI\ngoEs2rCbirin+T58djePtn2AZ3sOFpLsH/jJ45yLvYFFsLCt6lY2V64lmovxbP8eii3FTKbHWe5p\nZiwxis1kJ60mafas5MD4S+iouM2luM0eim2lDMR6EQURq8nBmpI2cnoORVVZ5qvDZXHw2IZ7+MeT\nz3PuxGnGvDES+QQxJYpZkLm76U5+57r7+a1n/5TeWA/+9BA2ycmjbZ/id667H4Cnzx1gKh3h4Pgx\nskoWh+zg7qadRLPTX0QZJUuDp3pON/VU1wFe6D9AWs3O0bQD/ODEngLf/tiGe+bw77NVLd9uf4bX\nR47SF+lmZXErGyvaMDDmPd7bxYUDsW+3P0NOUzgx2YlVsrKlet1/GT74WhwO/rjzVV4aOMzGitVz\n/nbea1yL1+Jq4fjx49x2222Lfv4lOfV4PM4zzzzDww8/DMCzzz6L2+2+6IJ3dHTw8MMP8+yzz1Jd\nXX3RfmZz6o+vs/LjkRcJZxNEMmGiuQRjqRESuelCl8rn6Qr14zYXkcgn6Y+O0hnuZCzVT1ZNomgK\nNa56mtwtjCQHpjtmNYKqK6TUKC7Zi2Lk0QwFzVDIqinOhk6xuWwL22pb2VTVwrqKRmRJ4u9P/JhI\nboKEGmQkMYJFLGJtWQtNvkamUhFuqt3OxvJWntj+6/SExvnWnX/EVDrOSGwSSTDjsfqoclQxlBhA\nY5pXr3bWkMwn0NCpc9cQy8b58vaHsMlmOvyDCG4z4VwMwwCXxU1OzTGSGOe1oQ6G40PYTE4soo1P\nr/t1fnPjPQVXw7ayBjoDw/RGBtEMjesq1/HI2t2cDY4Qy8YZiI3gNDvoDAwX+M9XBk9wLtQ/r6b9\nQh55IV65wz+IWbJgFm385a4v0h+dvGyOhRdypzN8+0QqQGtZC4lc8n21KvTd4FrkkV8f7sBrc5N4\n02b5Sv0ersVrcbVw2Tn1zZs309PTw+DgIFVVVfzoRz8q3BrMYHh4mPvvv58f/vCHNDU1XfKgpxN9\n+PVxJtOj2EwOjJhGNDeFQ3bT4lvDypJG2idO8vzAC5Q7KthWs5GD4/tI5EKouooiZNjVcCNHJjpo\ncK9gKj2OTXSgopJR0iTVKJX2eqL5EJHcODk9gWzY+Ktjf8qTZ3+ETXbS5Gnmz2//Ak2eZnpiRwED\nWZDpj/YymZokr+Ux0HHIDpxmO3t6j/Knt/4WNtmMQ7azs2EnQ9ERWkua0QUDVVcpsnqwSWZOTnXg\nT4+i6SpDsWoeWv3Rwnuf4ZN/c+N9/PEr36HcWcqrQ68Ry0WIZkPUOOvIawpP/tq3500qmh1W8dHW\nHXMUGA6zHd3QC5ppq8nMkfEOhuIDFNtLL9K0z5d1Ol/XPbP/J7Z9fEHFx+VSWszs22d1LyjpnA+/\nqkqPq/2+llbnvv9wyU5dFEVaWlp4+OGH+eY3v8kjjzzChz/8Yb7zne9w7NgxNm/ezOOPP86JEyfY\nt28f3/nOd/jBD37AZz7zmTn7md2p/83u5fBmlugqXxsT6VFEQSSjxslpOk2+ZuqKqtB0MIkyPaE+\nRuI9ZLQoGgp2kxebycO60pUEMxEq7VU4LS7C2SACAk6zhw+1fJDJZIhILkTGCKGQwcAgpkyh6Crj\niSGGYkn+dOd/53tv/Ot0V69PL+jRMQikRzAJMgPxHgZio/iTIRRVYF1FIytL6gim4zR56zk4doKh\n+Ch2kx1BEDgdPM1UepS8liGpBPBZqyhzVBJMxwsqiWj3KCsamwoqm6l0hKlMkLyWpdZVxz/c99VC\nyMWF6gObbC6EVVyowOgMDM/poPePdOC2FpFWclQ6K/nDGz95UVFYjNLlQnXKfIqPd6q0uNDjY2bf\nq0sb8KdiuGQHh8Y6L6m+eL/6vczGfH4nV/t9Xa1giiXvl/N4T7xf7rzzTu688845P3vssccK//7e\n977H9773vUUd0JAkVlSsJ5GPs6FiDS7ZSX+sD78yTJm9np31uzkx3sEtDds5NfUGsVwQSTThMpeg\nGDkUPU+JtYLqogrcNieVzgrGEhOAQZWzlmg2wq7lO+kIdOFPj2KT7MS06fAIGQcaORL5KVxyKZl8\nBptsxm2uIJIfw9ANBFFCN3R0Q8XAwGl2o+p5OqbaCaYDZNUcbquLaDbOkfEOmr3LOBPqRhAFkrkk\nwcwECSWEquepcbbiNBcxFB3hiW0fv+hazCguopkkeV1BFmT+avfjcz48C6kP5uvgPtG2k6+8+n1q\nzXaePP0yGCKqpuKyuGjxNfDk6Zcv6vbm68RmFobpuo4sijyy7tKDmsvd0c3cRfysay+GAE3e5W9r\nUdC1gGs9om8x+FVUBf2q48p7vzid3Ph//hUwFxJxTIaTzmAvZsnMaHKEEnsJpY4SzgbPklQjZNQk\ncSVAkbkEh8mNxWRjIDZIk7uRIquTiVSA/kgPWTVLg3sZ40k/hyZeIKXESKth7GLx9MIouZQaezM5\nPUexpRyb7EDVRA6PHyWrJbCaithcto2smsFicrHa18qOuhs4F+7GJFrwWYs5MXWa4xMnieZTpPIp\nIrkYdtlGXs0zEOsDwGetwGOtwGqykdfylDvLGYkF6Zwapjs0xjBRftjxHN2hcTqnhvnIqpvpCAyw\nqqSR/sjknI50voSc2Zp1k2iecxfQF55A1TUOj73BZCpASsnS7FuOIDBvtzdfJ/bvZ14imU+iGRor\nfU2sq2i85O/3wv1cSt88sz1q0RfswF8ZPMFIYoJINoKqaYXIv8Uc/1rA2+2y5+tMr8X3dSWw1KWf\nxzUfZ5d3uVE//wXWli9DliRkSWJjVTNZ1UR3uBevtZju6FkGo8PElRh1RS1EcpOsK70JVdfwWkpA\nFPFYfASzEV4bfp2pdIBgdpi7mz6Mz+bl4Mh+4koQzcijo1NkKqXa2UKLbzUPrLiXsUQIn60EA1hV\n0kQ8myOai9HkbeWOxlvIqCo+azF9sW56IwPIkgXd0KYzUA2DCmcl8XwCj8XNbQ03MBr3k1RSpJQ4\nLouPWmcdDtlJVsmwq/E2Do8d4tDEYU5PnaUjcIY6dx1doR4i2ThWk4VfDhzFn/QzlvTPKdIwvznV\nP5/+Kf7UJP70BCbMNPuWFUy5DMMgkU8xnvIjCxKRbJTO0FnKneU4LPaLBpvzUSkT8fichWGLGYRe\nuJ9LFbTFFLwO/yCyZCavavzF7V94y9zVazHq7FIReItZ2HMtvq8lXFlc84ZeqtXKuUDqop87ZDvl\njkpEQaTJs5KMmsUiWBmOd3N9+W4QBOo8y/lQ810IgsFEahQdnRpXLRaTBVm08XT3v9MT6aPFtwKb\nqQgBgQbXWrbX7GT38l1sq93Mg+tuY0XxCsLZIPF8lFeHj9AZPoluaDhkBx9ecRP+5BQHxl5iMN5F\nKp8goyRJ5hO0+FZR6agikAmQzCfYVLWGj7buYCA+wGCsl3BuCk3XODz5CiOxAdJqmtP+s+gYmASZ\nvJElr+Z56ZW9WGQr9Z46BmIjjMfHORk8wZngSV4Zep3dyzcXrst85lSJfBzN0DBLZm6q30IkGyuY\nSllNFho81dxcs5V4Pkkg7ccm2fhF7y/QVY0nT79cMKxayMTqk+t3c3fTTj573f0XBWYsFgsFa1y4\nfbJraEFaYSYA5APLb+THZ15a9DlcKyEZl4qsu9AMbEarvASWrsW7wBXv1CNeN/+xYxmnA3O7k5Ul\ndaiawEpfE/VFNZycOoUoSlS7llHhKKfMXsrOuuvJ6Dm6g33Uu5fhT/k5Gz5GRk3hMnlpLdnAZHKC\n/ng3WTWBSy7m4daHeGLbw0SzKbqDQ/yo83l6I93IJivjyWF6YqfRNBVJlKh01tDh76d98gCR3AS6\noZJRk7T41lFsK8EkmnDIdiLZMJXOKpxmF3t6DzEYG8CfGcTQNPzZITJalGjej0sqxiLbCKUDTKS7\nMXSRu5rvo1r3sHXlFp4feJnxxAixfAxFy6EaKruX7SaeyyzYucaycXKahs/i5Zb6m/hvG+4uSBqt\nZiuPrt3NhspGWssa2D9yGk3XMZvM2E1OEvnUHGuBhbrl2d3h7Of8yWt/wz90PMW/nH6O25bdQJFl\n4c75UrTBzPYN1lpaGuend2bOY99wx9uiMa72cHEGl+qyL+zkJ8bGlmiHNzE8PLx0Ld7ENR+SodpM\nqLpCIDV38GeTzYUFRyIiTtmNxWQhlU/S5K1nKD7J832vIEoSxTYfgiCQ1dKUO+oZT/RiNRXRUtzI\nYLyPJs9KTgT2kdPT/ODUD3i2bw8ri1dx0n8CXTDIq1ly2SxZPYGipckYURpsa9lY3oZZMqNjYDE5\n0XWVZu9GbCYbipbDITtQdZVwLsB4sp/x+Cj3Nt9FbVE9U+kxTCYT6WwCAwUNlaAyTou8GrPJilly\nkNOTHBs/xn88+Nc88eI3iOfChLKTYICiZ6lwLOdcuIcaZ1khim82Zssh9/a3c9+K7ezpayelpBmJ\nT/K1Wx4rLPU3Sxa+dstjBdlkT6SPek/dnM55oSHc7AGfiFjouHVDQ9EVYrkwH/vp53i47WMLDgH3\n9LUTzcbnHc7O/L4XO4B7u8PCqz1cXCwulIYuLbY5j6Vr8c5xxTv1WHUlB27ZcNHg7/df/Av+o/tn\n9EaGiaQT+Kw+hhODVDmqCOaihDJBgtkp+qJnCWQmEJGocdYxmZrAZfGxe9kdJHNJXHIRCSVBPB/H\nafKSUROYRAtTmQAJJUYgPURKjWE3FeE0ezAMKLPXs6n8OtZVrGTfyDFiuQSarvFI62fYWbeV10YO\nUGRxs9xbT4e/A0VTSCohFF3nVOgMRWY3oiBza/0HGE2OImFBFMy0Fm+hP9ZFODuGois4TF7K7NUc\nGjtLIpekP9ZNKh8krSXYXLaTpBKn3F6Bw2zHn4rRGx6fV1o4W2L4yuAJVF3DLlsJZZIE05FClxrK\nJPn8lgcIpuP8zuaPEs2m5nTOiwma9lrdFNs9PNR2Oz/u+iXxXIS8lqfJs5KJ1BQm0cze/sMXBXq8\nG1OwC/F2h4Xvl+HiEl++hMXgmufUS0sqL+IZJ5NBwpkQeT3LZGqAznAHoiQiIPBG8DCnp07SF+ti\nS9UWBMGgxbsGi8mGy+zEJMqYkNk/so9GTx3/c+dvE8mG8FpKCGT60Q0DDQ1JMFHnXI6m51lTsh2r\nZCeQHkTVs0iCidXFTfhTYVaXNuMwOah1LSeQnuL/O/VvDCe6ODL5Gi8NvMSdjbuwy06KrbU4zW5s\nop2eyBmaPc2sLm7guY//kBbvOjaX3oJFstDoWcXWyl1YJSeGAaG8n2x/GLtsxW0tRhItOCUvZ8PH\nkEUTjb4G+mOjBFJhvn38h7wyfJC9A6/y72deLVzD2ZyxiMiJyTN0THWxb/gYB0dPcHD0GCZRmhNF\n57M7LwqqmN1Nz+aeZ/PhH23dUXjdP977depdTXxqzaewyBYi2QhD0ZF5Az3m49RfGDzIT7qe4fsn\n/4kv7v1rMkp+UdzpYkI73s3zrxUs8cjnsXQt3jmuOP0iOhwX3XabJQtJJYKqKdhMdj6x6kGOTZ5A\nEiQcJg/JfJAV3o28MvgSAmZOB49hkSzcWL2VlJpiMDaAx1rM4YkTlDg85JQMwdwoWSOGrNmwiQ4i\n2SCRbACLaKM7chLFyCIiE9f8qEmFfWNHKLaVUFtUQbmzko1lbRyZOM5UZgKAhDKJP23iuYEXaC1p\nozvUhT89TkIJYDN56IqcwxBANXT++b7/VfCXOTLRQSAVoMxeh0k04TS7mEqH+LWanfRF+7GIDqwm\nJ1aTjY+tuJ/++CjpfIL2yQ5iuQhxJUqFvYrZDj2ztetVzjIsJpk2TwtHJk5gk+3Ioky5Y25u6Hya\n6YU08Au5KFa7fDz98b/mByf20OxbzkBkhD+//Qs8dW7/HM/2C/cxQwl1Tp0hmY+BaBDPTx+z5i3+\nBK/2aspfRSxd0199XHH6pb3CwZesA/yi5yA31m5gT187U+kIb/hPYZLMtHjWIAgCI8lRii0l6IJB\njbMRq9mGU3ahGSqJfIismuZcpIdkLoUoCDjNLuK5GKOxSd4IvYJipNHIIWEFQcQwNDJakowWQxLM\nGIZGUg8A+pv2Agp3LNtFqcNLlaOCtJohnIuRUXLE8n4EJMySnXg2xJnwMRJKjKgygWpkKJLLSCoR\nKp212E1Wftl/BKfZzs97XqQv0s1keoRqZwOKrpDTcyyva+FMsBuH2UFeU7DLTj7Ucjef2XwPw7EA\no0k/kWwEzdCoddWzpXL9HGnh7AHbo2t3E8lkSeSTRHJxmn3LSKs5RuLj/N/2f+GX/cfwJ6a3qbpG\nLBvnud6D9EUmeKZ7L2MJP9H8ND0z22/9rWiBlSV1TKXifOn6j1Nktc0ruzwbHOGB1Tdjk80FKiaY\nijCVGafW2cj1VRt4ZO1uGpctW/Bv5koNPK+WZ/iFuBKDwWtliHwpLA1Jz+Oa16mfbijh9TVVRHIR\nnu1+nf2jRzgZPE0iH8Zl9uG0uJBEE9dXbiKci3Jf4wdIqTlGEyN0RY4xlRlGN3QUI4thgKrn2Vxx\nPbuW3cRx/ykCGT+h3DAqaUzY8Fmq8FlLCWSG0Q0VEROqkSZtRNHIYSAgIFDrWMmp0Bn2jx4kpaqk\n8xm+tvO/s6dvH1bJSSQbIK9l0AQFi2QnqU4hAhJWdDQ2lt3AypImHBY7owk/PdF+OoPHiCtT5PUc\nKTXNKm8rN9ZspTc6QCDjR8eg2lnLR1bchc/m4dBY57SXeVE1um7wzTv/EJvk4JG1c93xVpbU8Vzf\nITwWF+dCY3xoxQ2EMkk+u/kBotkUg7FxzgRPMZEaIq1kSCo5Erk0dtmK1WzFbXGhGhrjST8JNc6G\n8nVEs6lFfcCf6jrA/pEOdAPWlJ1fazCfWmamaMx8CdW5q9hRfzNtJSsKwSjz7X+mwGq6QTKfekvj\nsMtRkN8vhe5y4FLa+SVce7jmOfWUyUxKSZPIxbGYzIynh0jmo2CAxWRje/VmrqtYh2qobKpay4Pr\nbmNH/WYCmTFkwYqAhGaoSMiktCCqrtAb7eeDLdvQDZ1I1o+ICRkHVtx4rGWUOyppcK2i3N6ASTSj\nGiomZCQcmLFS71jPVHqMiWQfwcwI+8ee40yokxf7jlHpqKLUXkG5fRk2k4sScy2qlkdEwiJ68Voq\nuKFyFzdWX0dDUSWV9hLOhc4wEOnFMAwEzFhMdu5qvIdQNsSRiRP0dZym1F7OWHwAzVBIKzn8qRA5\nTaHWXU0il+Sbdz5Btcs3Lze8p68df9LP0YmTjCX97O1vn8ObK1oeRVfRDBVDMFhXtoqv3fJYYZbh\nNDs4MdnJVMaP1+zFbjIjCgK/8/xf8hvP/L98++h/LqjvvlTQ8nxc+oxe+7PX3c9/23Anj67fVXhP\nF3Kns/fvMFsuGW49Eve/6+DnS2nqrxSuBI98Ke38tYIlTv2d44pz6i3VGymzVrCzroaTU2fQdJWU\nEmVT2Q7ubLqFB9umfYNnc7rhTAxRMJFUg+SIYcWHjoKADEA0F+Irr/49H2m5h7899pd4TFVktATV\nzmYaXMtwWVxYTXZGE8OIWRMa0wXLKRZT5Wgir+eQTVYEVSSgn0NEpD+W5oX+ZUgmM1aTlZXFrRjA\nWHwYTdBxSMuJKzE2lG1hU2UbSSVNieQlko0hihITiX5ETIiGRLN7E1PJAEklztnIcfRMjmOTr1Fq\nryOhpNg/dpQicxG1RRWMJcZpK12xoBQQmJOCNBAZ4feun+srs6VyPVktS7Owgltqt/Lg2tvnSAg/\n0baTI2MnubPxA5wJdFPuKCaciRHORsgqWfaPHcVjc84rOTRLFg6NvcFIfJjaolqimSSfXH/+TmKG\nSxcF4ZLuj/NhthzxwlDt2e9/ZhYwEp+ktqhiTkF+u7zxtZwzermx5OXyq48rL2m8aSeWHTeyf/QY\ng7F+wplJHGY3mgFpJc8/d/wne3oPcmjsOKF0hq7gKJpuEErHyag5LEIRiOCzVpNQprBKTjRdQTHg\nXKSHcGYSt6UMEYFmXyuxfJyucCedoYM45WIyagrBEDGLFm6vvY+8riKIArWOBqJKlKyaREDEJFiw\nyEVsqFiDhMTXb/0c+4Y78Fp9dEWOk1BCuM0lVDlrGE/6mUgFqHSUISAwFg+QUOIUmX0UWX1oaHgt\nPqayUySVKEpRHgOBcHaEqfQE1fYGvnbrZ4nnMjjNDnRDv+TyeZNoZig2zLaqTfRGJuZQD61lDWDI\nPLHtIbbUrLzoFluWJAKpJOl8mjpvNY++6cneGxlkMj2O3eSg0lFBa1kDz/YcnkNvrClbxov97Uii\nxGBikFOBM5z0D3Frw+Y5VMzri1wwdCF3+nYzTr+45WOEMsk5z3+7dMq1Ii1c4pHPY+lanMc1z6lb\n7rmbb0iDRLNxBuM9yJIZm8lGPBei0lFHZ/gYk+kxpjKT9IT7CGXiRPMpnGYneV0nmBlB1RUcZg/r\nirchixYailpwmG1MpsbRdA1Fz7Gp8gbubNzBeMLPSLIfRc+SyIcQkRAEEbPopKqoDqvJylCij4H4\nWRQthyiYkDAjiTI5JctYYpKba67Hn45yLjzAkcn9ZJQ4BjoucykfWnEHgWSY1rIWUkoGr9VNLJfC\naXIRU5OU26q4veFmGtx1BFJhwrkgHnM5NsmBKFgotlVRbCvBappWBV1onztfoZmx/q1yViKIAofH\nTvBifzuBVJKVJXXs6WsnmI5wNjhSKPZ/+OJ3+aeOnxcG1Bsqm+YUz+7QGKOxSZK5BNurt5LTcvhT\nsTm6d38qxobKRgKpJH3RIYZiPUiSjEmQ0XRpjvHXO+VuF1NgZxf+Iqvtoucv8cZL+FXCNc+pjyoi\nPeFeBuO9ZNQoujYdbNFWfB2NvgYERMySFQGm/y+IVLsq2F69AXSNNSXbccheKmy1fHjFHazwrcJp\ncaHpOoIh0OhdzZbKm/jb3U/wyLpd2EwOdF0HAxwmH59a+xgmQcZjLeFs6DT+lB9Vy2MRbJhEExIS\ngiBQZqklrcVQDJXDk2/w0sBhVpc2Yxg6kmBC1XOklAiZXJaNFatRNbWg6/6LXZ/jg82385trHqXR\n04DFZOF0sBuX7GBbxS3sNLawuXIba0o2YRHNaGhEM0kySp5PtO0knI0jIV6kH5/hkp88/TL3rdiO\n0+wgo2RRdIWm4voCrzwf7310op1jgUO8PrqHB5/6MsAcvj6SjbGmfCUljjLOhLoLWvljE53E86nC\n4x+c2MOHVtxAlbMSSZTBgLyeL0guZ84xrypUu8rmcLfzebK8E+70Ujr0K80bXy6vmSUe+TyWrsU7\nxxUv6geC3UzER4nnQsiilTJHDRXOWpyyDX9yis0V21E0lUpHAxktRWfoOL/s30tcSSKKZsYSQxTb\nyvnuPV8lqaRYVdrIcm8teTXPSt9qqp1V/NWuL+GzO3mq6wArixupc7XQ7NnEo22/gUkQEQWBcG6S\nWC7IPS0foMbVhChKZLQ4ZY46KuzLSWoxDEMlkBrgZKCds6FOjo4dp61kIxWO5VilIiySg5+cexoJ\niWMTHbSPvsFHfvI432p/BkXXeXDt7bQUN7yZRuRHEEWafPU4LXZubdhKkbUIWbKyrrSNaC7G0+cO\nXDQEnSnKM3a7B8aOF34+U7x21G4tfKnct2I7ZsnCiclOTk11Ec9Of1moqGS1FDo6HrP7oqHizLBw\nU8VadjXcSFtJMwYGte5qwulo4XEgFeTr+/+JUDqEx1wMho7X4sEqm/l2+zM80/0SSSVDNBdDluR5\nveHfzVBzMbjSi4+u1Pt6r3CtGKAt4fLgitMvh27YxDFvFtVQKLL4qHcvx2kuYm3ZalwWO5FsjGpn\nDaIgEclOEVemUA2N0XgARc+R1dLc1rCLnKryxuRZzgTPEcsn2Fq1keqiCpyynVAmSVtZA9888iMG\nosNYTVaqXNV4rUXTHiaqTDAXpNnTysbyNfyPG36DF/qP4TKX4LH6wDBodLeQUFKIgoSq55FFM1OZ\nAKJgIpYPYRhML2ASJAxBRjN0xpKj9ESPcczfTjKnoekSgiARy8Y5E+wikJmkJ9LH5pYtJNUMwXSE\n8eQobwSOoxhQ7agglIkxnprWqefV8x7i3zzyI7rCXUymxjAJFh7f9omCXcBMStDsrNEX+9sLlJA/\nFaPeXccp/xkaPavZVrOZR9funkNLzFAaj67dzebqFjqnpmkgh8XOl7c/RHdorEBpuC0uxlN+NEPH\nJMl874NfpX2ii5ymMBAdZioVps5bfRH1MR8tciF3+k4lilf6dbNxueieq8UjX4uSziVO/TyueU69\nY9dWJqtKKLdXcnPtjWwsb+WE/zTt/qMMxIa5qfp6JtNTjCVHSOQjCIIJq+TCLJqpLqrFarKDIfCl\n6z/Od47/G6dCR/AnJ5hMhahwVhU8w5/tOczTPc8xEO8mkU+gaBrDsRHi2ST+TABRNFHuKKfFt5x/\n7nyWrvAZdHRiuTB3N96NZhiklSxxJUxajeEyF9PobcEmW3HKbuJKDEkQafSspLl4OQdH9zOY6CBt\nBEEXMQSZ6yo28rG2W/CnYoQzCXpjXYiY6IsO0hvpYywxSrm9kryeRzd0xhN+TgW7aC1dja7rczzE\n//3sSyBAVsvyoaY72FKzElhYNx5IJUnkkoUwalmQ2V69hbXlq+bViD/bc3gOD7+mbNmCodTdoTFM\nohlN0/n7u7+Cz+4sFLaaokrWla/k0bUXJ88vZgj6TgvMlX7dbLxfvGYWwtIM4trGNV/URz5yL2Ur\nr8OfDNPoqeUTa27jH089RSTnBwNsJheSYGJz1QbGY7TW7gAAH7tJREFUE36cJi8rilvZvewWnBYn\neVXj1vrrOTp+lheGXkA1VDJqDE1XSeZzfPXmxyiy2qZTdbJJxhNDuMw+vFYvo8lBeqMdjKd6iOQm\nyGuwf+wAFtFOPBcnqyVxyW4k0cwyTw0DsUEkUcZl8rGxYjNbqzYyGB9FN3R2N+ymyFICwKmpU+iG\nQTg/hBknCimsopP1ZZtYX9HIhspG/u7Yk0SzAdJqHG0gxwc330t/ZBCfzUuJvRQBAUmUWFe+hmQu\nyV/u/sKcnNKzwV4m0+PcvfxOPrPpnkuGUcwUmhk1TTKfYjThZzA6ytPdr+JPxFldunCoxYbKxgVz\nSWcGtTMrSmcf75G1u9lU1bLowIcLsyjfaYFZ6HWX6sQvR0FbzHB3MXcEVyuX81r8UlrKKD2Pa76o\nVz3+P/iO/xDRfIxDY0c4NHKWnuhZZNGMKIjc23IHNUWVpPNpwESJvQSHbGc0OUHH1Cl21myj3X+a\n7mg/48kRcmoK1cggSVZEwYTN5GFjZTMd/kHMkoVQNk6Ns5qJ9Djx3HTX/aYxABktiaLkGEp0kVSm\nKDKXY5GsrC1bg8vqZLVvJRlFodJZxZryFciiRFrJIokmmjz1fH7LR3lt6A36YueYTPeTNzKISIiY\nKbHWEcrEULVpVcjevnbSagabyYklKZGyK3jtXm6r284Xt36Co+PnWOatx2Nz8eXtD13kmuixeMiq\nCuvLVrG5uqWwbaYozXTknYHhOY6Os9U0bouL3sggSSXJRHIK3TAVnCCPTXRila3zpiNdiPmK2DuV\nBV7om/1OC8xiHCfn68SvVEFbzB3B1fIQv1YknbOx5Kd+Htd8Uc/+1m/xk6kOkvkkoUwAn60El7mI\ncCbER1d+lM9s/CCD0Ume6d3LZHIMu+ygO9JFX7QLDEiqecYSI4iChNvso8RaSV7TAZ1QdpRTgXOI\nhoszoT6OjB2hxlWHJEhcX7WFs+GzpJUIOhpgYBe8GIJGtWsFqqojmyw4ZBcHxl9hPB6gydfI2rIW\nPDY3p6e6ORM8x0hylOsrN5FWM4QyScocJbw2/DICAhbBgUUqotrZRF7L4M9OoOkmguk0ZTYffdFh\nKl1VFJdXYDFZaClupMJZwnXVLdzasJlgOj5vcenwD5LIJ6nzVC/Ihc/Wt894u3T4BwsWAjO0SW9k\nAE3X2Fy1jkfX7mb/yLSe3GKyEslEL/pCWQgXSiQXes2lOtQLP7jvtMAs9LpLdeJXqqAt5o5g5lpc\nK140VxNLBf083m5RFwxjtv/fe4cXX3yR226/ndjx4/zd1Gn2jx1FR2dlcTM2yUy5oxizZCaSjfGz\nc8+RUGJMpAYwDBVFzyGLVvL/f3tnHhxXee7p53T36b0ltZbWvlirJVuWbOMFzG4bUzAYAiRj6obx\nzZAZhgoBMglJZjJ3YG6qEsgNNcOQzA1JxSkSJlzIJIFcYhuC2RwL22DLqyxbtvaWulst9b6fZf4w\naiRbXuRYkrH6cbnKap0+5/Orr1+953feRQlj0GZRbqmn2FbKiuIWvrbiXr629Ue0Db9LNBXCYSon\nmBpFUhKYxGxURSWlxCg0V+KwFGLUmdg9tAODYCauRLCJuZRn1zAQOkVN1kK6/Ecwi1koqoSiwori\n1SiKymhsDFGrwxUZQlFUFtir+V/rv8Vfuvfxw49+TCIVYWH+MtYuWMPOvt0MhgcotpSxumw5kizh\niY5xwH2QYmsxKTnFWGIMVBl/3IfZYKMmu57n1j1Ortmattl4ZSSqBovekLbPxErJ8WP2DR8lISeQ\nVZmRqIdcUy7uqIua7DquK1vOA4tvAeB3Rz9AEEhXa25pfyvdYbHEks9YLHBRlZibX3+auJwgKkWp\nzanhf254bMrjfvbJn0jIKWKpOFU5pResZrzcXQRjqeQVUS06nXVM12YZrm7279/P2rVrL/r42Y/U\nn3iCRQsWo6g6arIrOerpoiq7lAea17LbeZR2VweHRz/BF3eh1ehIKjEsOjsx2Y+ABrNoZzQ+zEjM\nzZryNSwrqufWqhW833uIaCpCTA4Tl8PElRARaZSgPIhJyGUk3oc/PkZSlkGFqBzEoLVQk92EANxV\neydRKUE4ESWQGsWgMVGT08CSgkbMejMH3PuISBG8MRdWvY3WwhaCiRj+eJCanHrcMT/31/8bNrdu\nQFK0LC9aSmV2GZFUDKPeiN2QRTgVI5AIkOwOUl5ehVYjMhA+STQVYig8wI7efSQl3VmDJsLJCHnm\nHPzx4Fm38O/3ttPuPoY36qXLd4wSaynHRtvxRIdRVcgzOTDrjGmdvKXo9N+JYwTH5Yfdg0cv+qHh\n1q6P8CV8mEQz/7T28Um56BOjzImj9qaKUM/UTi93JsaVIi1czDrGbZF5cJnR1CdyxcsvsSefRDSb\nWeyoom3wCHZTNqFkBHckwAHXMfZ5PiGYGEGnMaACBaYKJDWJoqjoNAZARdToabC3MBr1o6g6VpTW\nI2os/NW5m4QUJqJ4kAiikAQ0xNUgIGAT85GUJKGUj5gyhk5jArT8fcsmjDojRq2e+rw6cg2FVGZV\nISMzEByiMrsEQdDTHehEUlJoEU+nXtpKOOA6htVgpaVoEV9pvR2TqE87zomphuMZI5Is8/dVt2Ev\nLKbb14c76kJGIiGHEDVm3JGxdHXmmR/uqRzkIXcvRzwdaDU67MY8BkK96HVmdIIeq2hjeclS+oJD\nWEQzR0f6z7qdn+hszrzeeIuA3xx6i5NjQ2m9XtRqub58KW92fciakmvoDXjOOfHo/qYbcUcCZOkt\n7B48epakcKZ2eq5nBPPBsY3b4kp8cDnbZDT1z7jiK0oxfTas+MzueNX2Csw6K6LGiEyKRXkryTHm\nI2r0FJkrsYp5CKoGu6EEX3yElJrCHwvz2tEP+HPXe+To89BpjGgxIWAEPu0PjgktIqqqklIS6DUW\nbKIDSYlRa6/j/qabTldyxgL0+geJywkCiSAL8+vSAycGggOEUmOEU2P4Ex5s+mw+Hj5Isa0QX8w/\nZeXkeOWnSdTzwOJbqM+t4Lbq6+nLjpGUUqyvup7Hl3+dbDEfozYbb8zJYLA/XZ15ZmWkRTTSExjA\nKBjSNrSIRnxJP4qq0FrUTGN+M+uq1pFndnB79XpcoREa7AvShUPnK44583rjRTXD4SEOuDsmvT/X\nbGVD9U1otdrzTjwaLwQaiwWmLNA5cxbl+BoWFzR8WrT1+SzouRTGbfF5ndx0OcnMKL10ZrVLoyqK\nIIrpr8/sjnfKN4jdYKcvmKDBvgytINCY28BIdBAEDUadmdbCFTjDg4zFRzgx1kGPvwt/YgS91kRS\njqLIErliCWMpJ0ki5Ovq0Gn01Nmbselt9AW6CcbHSCpQYqvlmXVPpD881fYydvZ/TF+oF1e4h32e\nNpYUrOTOumvZ0dtGf8iKUWNGK+jp9B3CoDUxHB7mrtoNk7oqTjVRaPyDOq6XtruOMhIdQVYlYnIE\nVZVREaix1/PFRTcBZ3fU88UDNOXXpatPNy2+GV88wIbKWzk40kGZ1cE3Vn2RN463kW/KOV0RmlVE\n96cj5y7UWvbM66U7JopGqnLKz3r/VAOez9Xx8GKGXI/bb9Pimydp/Vfy8Ojpkpk8lGGmmVX5peoP\nfyDxxBPp184seOkNuPEnQqRkBXd0mFJrBU0F9UiKwAnfYSJSAElWKbQUUWQpoTd4HJkUsioTSnlQ\nkSk0V7O8cBXDYReV1kX4Eh40ggazmI1GEEipEqLGgCIoFFpKOOjqTncY/M2htzjqPcxo3IVWo0dV\nFcZiXt7p/pg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       "text": [
        "<matplotlib.figure.Figure at 0x8fe7830>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Summary"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In this section, we investigated how to generate random samples from a given distribution, beit discrete or continuous. For the continuouse case, the key issue was whether or not the cumulative density function had a continuous inverse. If not, we had to turn to the rejection method, and find an appropriate related density that we could easily sample from to use as part of a rejection threshold. Finding such a function is an art, but many families of probability densities have been studied over the years that already have fast sample-generators.\n",
      "\n",
      "It is possible to go much deeper with the rejection method, but these involve careful partitioning of the domains and lots of special methods for separate domains and corner cases.  Nonetheless, all of these advanced techniques are still variations on the same fundamental theme we illustrated here."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "References"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[Exploring Monte Carlo Methods by Dunn, 2011](http://books.google.com/books?id=ACTrrQk1UgoC&dq=Exploring+Monte+Carlo+Methods&source=gbs_navlinks_s)\n",
      "\n",
      "[Continuous univariate distributions by Balakrishnan, 1995](http://books.google.com/books?id=0QzvAAAAMAAJ&dq=continuous+balakrishnan&hl=en&sa=X&ei=vzcuUtqvOYOKjAKr14BI&ved=0CC8Q6AEwAA)\n",
      "\n",
      "[IPython Source Notebook](https://github.com/unpingco/Pig-in-the-Python/blob/master/Sampling_Monte_Carlo.ipynb)"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}